Trigonometric Identities Quizzes, Questions & Answers

Dive into the world of Trigonometric Identities with our engaging quizzes! Read more

Pythagorean Identities Quizzes

Ready to turn sin²θ + cos²θ = 1 into fast answers? In this quiz, you’ll use the identity plus quadrant signs to find missing sin, cos, and tan values fr...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
If sin²(θ) + cos²(θ) = 1 and sin(θ) = 3/5 with θ in QII, what is cos(θ)?

−4/5

4/5

3/5

−3/5

Pythagorean Forms & Trig Identities Mixed Practice Quiz

Put it all together—proofs, simplifications, and quick evaluations using the Pythagorean family. You’ll flip between tan/sec and cot/csc forms, verify identities, and u...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Which identity is equivalent to 1 + tan²(θ) = sec²(θ)?

Sin²(θ) + cos²(θ) = 1

1 + sin²(θ) = csc²(θ)

1 + cot²(θ) = csc²(θ)

Tan²(θ) = sec²(θ) − 1

Proving the Pythagorean Identity Quiz

Go from “know it” to “show it.” You’ll prove sin²θ + cos²θ = 1 from the unit circle, generate the derived forms (1 + tan²&t...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Which expression equals 1 by the Pythagorean identity?

Sin²θ + cos²θ

Tan²θ + 1

Sin²θ − cos²θ

Sec²θ − 1

All Pythagorean Identities Quizzes

Reciprocal Identities Quizzes

Reciprocal Identities Proof and Simplification Quiz

Flip with confidence. You’ll prove and use sec = 1/cos, csc = 1/sin, and cot = cos/sin to rewrite, simplify, and evaluate expressions—no fluff, just smart substitutions...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Which reciprocal identity is correct?

Tan(θ) = 1/cos(θ)

Cos(θ) = 1/sec(θ)

Sec(θ) = 1/sin(θ)

Csc(θ) = 1/tan(θ)

Reciprocal Identities Unit Circle & Domain Quiz

Know where functions live—and where they blow up. Use unit-circle coordinates and radian angles to decide when sec, csc, and cot are defined, evaluate exact values, and solve...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Which reciprocal identity is always true?

Tan θ = 1/cot θ

Cos θ = 1/sec θ

Sin θ = 1/csc θ

All of the above

Reciprocal Identities Application Quiz

Turn definitions into shortcuts. Expect quick simplifications (like sin·csc = 1), sign checks by quadrant, and triangle/unit-circle setups to evaluate sec, csc, and cot. You...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Simplify: sinθ/cscθ + cosθ/secθ

1

2

Sinθ + cosθ

All Reciprocal Identities Quizzes

Quotient Identities Quizzes

Quotient Identities Proof Practice Quiz

Lock in tan θ = sin θ / cos θ and cot θ = cos θ / sin θ. You’ll prove small equalities (like tan·cos = sin), spot non-identities, a...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Which identity is correct for tan(θ)?

Tan(θ) = cos(θ)/sin(θ)

Tan(θ) = sin(θ)/sec(θ)

Tan(θ) = sin(θ)·cos(θ)

Tan(θ) = 1/cot(θ) only

Quotient Identities Simplify & Verify Quiz

Speed round: convert between tan, cot, sec, csc and sin/cos to simplify, verify identities, and evaluate at common angles. Expect reciprocal/quotient swaps, cancellations, and quic...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Simplify: (sin x)/(cos x)

Sec x

Csc x

Tan x

Cot x

Quotient Identities: Radians & Unit Circle Quiz

Connect the algebra to the circle. Convert degrees↔radians, read (cos θ, sin θ) from the unit circle, and use quadrant signs to evaluate sin, cos, and tan. By the ...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Convert 225° to radians.

3π/4

5π/4

7π/6

9π/8

All Quotient Identities Quizzes

Co Function Identities Quizzes

Trigonometric Identities Quiz

Trigonometry is one of the core branches of Mathematics dealing with angles and calculations. This Trigonometric Identities quiz will gauge your understanding of the complex and in...

Questions: 10 | Attempts: 9580 | Last updated: Sep 05, 2025

Sample Question
Which of these is the identity of Sin 2x?

Cos^2 x + Sin^2 x

2SinxCosx

SinxCosx + CosxSin x

Sin^2 x

Secondary 3 Express Trigonometry Quiz

Get ready to tackle the "Secondary 3 Express Trigonometry Quiz," a formidable test of your trigonometric prowess. Trigonometry, a crucial and demanding branch of mathemat...

Questions: 10 | Attempts: 7385 | Last updated: Oct 16, 2025

Sample Question
In the diagram below, a diver is to retrieve an object that is 14m away from the wall of a swimming pool. It is given that the angle of depression of the object from the pool platform is 30°. Find the vertical distance the diver has to swim in order to retrieve the object, correct to 3 significant figures.

7.00m

12.1m

24.2m

8.08m

Trigonometric Equations & Identities- Assessment Quiz

How much do you know about trigonometric equations and identities? A trigonometric identity includes trigonometric functions and is valid for each value of the happening variables ...

Questions: 10 | Attempts: 525 | Last updated: Mar 21, 2025

Sample Question
Equalities that involve trigonometric functions and are true for every value of the occurring variables are called...

Trigonometric identities

Numeric values

Identities

Values

All Co Function Identities Quizzes

Even Odd Identities Quizzes

Even–Odd Trig Identities: Proof & Verification Quiz

Are you ready to discover how flipping angles affects trig functions? In this quiz, you’ll explore how sine, cosine, and tangent respond when you replace θ with −...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Which statement is always true?

Sin(−x) = sin(x)

Cos(−x) = −cos(x)

Tan(−x) = −tan(x)

Sec(−x) = −sec(x)

Even–Odd Trig Identities: Apply & Simplify Quiz

Can you simplify tricky trig expressions using symmetry rules? In this quiz, you’ll apply the even–odd identities to expressions that mix positive and negative angles. ...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Simplify using even/odd: sin(−x) + sin(x).

2 sin x

1

2 cos x

Even–Odd, Unit Circle & Radian Understanding Quiz

Ready to connect even–odd patterns to the unit circle? In this quiz, you’ll use radians and coordinates on the circle to explain why sine changes sign but cosine doesn&...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Convert 150 degrees to radians.

2π/5

3π/5

5π/6

π/4

All Even Odd Identities Quizzes

Double Angle Formulas Quizzes

Double-Angle Formulas: Simplify & Evaluate Quiz

Now that you know the double-angle formulas, it’s time to apply them! This quiz focuses on simplifying and evaluating expressions using double-angle identities. You’ll ...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Simplify sin(2θ) when sinθ = 4/5 and θ is in Quadrant II.

24/25

−24/25

7/25

−7/25

Double-Angle Formulas: Identity Proof & Derivation Quiz

Get ready to explore how one angle can double the excitement! In this quiz, you’ll prove and derive the double-angle formulas for sine, cosine, and tangent — including ...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
Which identity is correct for all real θ?

Sin(2θ)=2 sin²θ

Sin(2θ)=2 sinθ cosθ

Sin(2θ)=sin²θ−cos²θ

Sin(2θ)=1−2 cos²θ

Double-Angle Applications with Pythagorean Identity Quiz

In this quiz, you’ll connect double-angle formulas to geometry, triangles, and the unit circle. You’ll apply sin(2θ) and cos(2θ) to find missing trig values...

Questions: 20 | Attempts: 10 | Last updated: Oct 31, 2025

Sample Question
If sinθ = 3/5 and θ is in Quadrant II, find cosθ.

4/5

−4/5

−3/5

3/5

All Double Angle Formulas Quizzes

Half Angle Formulas Quizzes

6th Grade Math Formulas Quiz

Are you in 6th grade? Do you find math an easy or tough subject? Well, we have here a special 6th grade math formulas quiz for you if you find it challenging to remember different ...

Questions: 10 | Attempts: 1487 | Last updated: Oct 13, 2025

Sample Question
For the area of a parallelogram, what's the formula?

B= (AH)

A= (BH)

H= (BA)

A= (2BH)

Sine Half Angle

Ready to take big angles and cut them in half? In this quiz, you’ll explore the half-angle formula for sine, simplify tricky expressions, and calculate exact values for speci...

Questions: 20 | Attempts: 10 | Last updated: Oct 24, 2025

Sample Question
If cos θ = 4/5 and θ is in quadrant I, find sin(θ/2).

√5/5

2/√5

3/5

1/√10

Cosine Half Angle

Did you know you can find the cosine of half an angle using only the full angle? In this quiz, you’ll practice applying and proving the half-angle formula for cosine, while w...

Questions: 20 | Attempts: 10 | Last updated: Oct 14, 2025

Sample Question
Which formula expresses cos(θ/2)?

±√((1+cosθ)/2)

±√((1−cosθ)/2)

±√((1+sinθ)/2)

±√((1−sinθ)/2)

All Half Angle Formulas Quizzes

Sum And Difference Quizzes

Trigonometri Jumlah dan Selisih Sudut

Explore the intriguing world of trigonometry in angles and their relationships. This quiz assesses your understanding of sum and difference identities, focusing on acute angles and...

Questions: 5 | Attempts: 457 | Last updated: Mar 20, 2025

Sample Question
Diketahui sudut A dan sudut B adalah sudut lancip. Jika cos A = 4/5 dan cos B = 24/25. Tentukanlah nilai cos(a+B) ?

1/5

2/5

3/5

4/5

Trigonometry Quiz: Angle Addition And Subtraction

Trigonometry is one of the most studied branches of mathematics. Are you ready for a trigonometry quiz? We have one here for you. As we all know, trigonometry is known as a math br...

Questions: 10 | Attempts: 261 | Last updated: Aug 16, 2025

Sample Question
Cos 105° =

(√2 - √6)/4

(√2 + √6)/4

(√2 + √5)/4

(√3 + √6)/4

Exact Evaluation with Radians

Are you ready to calculate exact values without the calculator? In this quiz, you’ll use sum and difference identities for sine, cosine, and tangent to evaluate tricky a...

Questions: 20 | Attempts: 10 | Last updated: Oct 14, 2025

Sample Question
Evaluate cos(π/12) exactly.

√3/2

(√6 + √2)/4

1/2

(√6 - √2)/4

All Sum And Difference Quizzes

Trigonometric Identities Quizzes, Questions & Answers

Popular Trigonometric Identities Topics

Pythagorean Identities Quizzes

Reciprocal Identities Quizzes

Quotient Identities Quizzes

Co Function Identities Quizzes

Even Odd Identities Quizzes

Double Angle Formulas Quizzes

Half Angle Formulas Quizzes

Sum And Difference Quizzes

Top Trending Trigonometric Identities Quizzes