SOHCAHTOA Quiz: Defining SOHCAHTOA

1) What does SOH in SOHCAHTOA stand for?

Sine = Opposite/Hypotenuse

Sine = Adjacent/Hypotenuse

Sine = Opposite/Adjacent

Sine = Hypotenuse/Opposite

SOH means Sine = Opposite/Hypotenuse. Example: if opposite = 3, hypotenuse = 5, then sin(θ) = 3/5 = 0.6.

Explanation

SOH means Sine = Opposite/Hypotenuse. Example: if opposite = 3, hypotenuse = 5, then sin(θ) = 3/5 = 0.6.

2) Select all correct SOHCAHTOA relationships.

Sine = Opposite/Hypotenuse

Cosine = Adjacent/Hypotenuse

Tangent = Opposite/Adjacent

Tangent = Hypotenuse/Adjacent

Cosine = Opposite/Adjacent

Correct ratios: Sine = Opp/Hyp, Cosine = Adj/Hyp, Tangent = Opp/Adj.

Explanation

Correct ratios: Sine = Opp/Hyp, Cosine = Adj/Hyp, Tangent = Opp/Adj.

Submit

3) What does CAH in SOHCAHTOA stand for?

Cosine = Opposite/Hypotenuse

Cosine = Adjacent/Hypotenuse

Cosine = Opposite/Adjacent

Cosine = Hypotenuse/Adjacent

CAH means Cosine = Adjacent/Hypotenuse. Example: if Adj=4, Hyp=5 → cos(θ)=4/5.

Explanation

CAH means Cosine = Adjacent/Hypotenuse. Example: if Adj=4, Hyp=5 → cos(θ)=4/5.

4) The tangent of an angle is the ratio of the opposite side to the adjacent side.

True

False

True. Tangent(θ) = Opposite/Adjacent. Example: tan(θ) = 3/4 = 0.75.

Explanation

True. Tangent(θ) = Opposite/Adjacent. Example: tan(θ) = 3/4 = 0.75.

Submit

6) The cosine of an angle equals ______ divided by the hypotenuse.

CAH means Cosine = Adjacent/Hypotenuse. The numerator is 'adjacent'.

Explanation

CAH means Cosine = Adjacent/Hypotenuse. The numerator is 'adjacent'.

Submit

7) If cos(θ) = 12/13, what is sin(θ)?

5/13

13/5

12/5

7/25

Using sin²(θ) + cos²(θ) = 1 → sin²(θ) = 1 - (12/13)² = 25/169 → sin(θ) = 5/13.

Explanation

Using sin²(θ) + cos²(θ) = 1 → sin²(θ) = 1 - (12/13)² = 25/169 → sin(θ) = 5/13.

8) If sin(θ) = 3/5, what is cos(θ)?

4/5

5/4

9/25

3/4

Using Pythagoras: hypotenuse = 5, opposite = 3 → adjacent = 4 → cos(θ) = 4/5.

Explanation

Using Pythagoras: hypotenuse = 5, opposite = 3 → adjacent = 4 → cos(θ) = 4/5.

9) If sin(θ) = 4/5, what is tan(θ)?

3/4

4/3

5/4

9/25

sin(θ) = 4/5 → Opp = 4, Hyp = 5 → Adj = 3 → tan(θ) = 4/3.

Explanation

sin(θ) = 4/5 → Opp = 4, Hyp = 5 → Adj = 3 → tan(θ) = 4/3.

10) If tan(θ) = 3/4, what is sin(θ)?

3/5

4/5

5/3

4/3

tan(θ) = 3/4 → hypotenuse = √(3² + 4²) = 5 → sin(θ) = 3/5.

Explanation

tan(θ) = 3/4 → hypotenuse = √(3² + 4²) = 5 → sin(θ) = 3/5.

Submit

12) If sin(θ) = 5/13, find tan(θ).

5/12

12/5

13/5

5/13

sin(θ) = 5/13 → Opp = 5, Hyp = 13 → Adj = √(13² - 5²) = 12 → tan(θ) = 5/12.

Explanation

sin(θ) = 5/13 → Opp = 5, Hyp = 13 → Adj = √(13² - 5²) = 12 → tan(θ) = 5/12.

13) If tan(θ) = 1, what is θ?

30°

45°

60°

90°

tan(θ) = 1 when Opp = Adj → θ = 45°.

Explanation

tan(θ) = 1 when Opp = Adj → θ = 45°.

14) Choose all correct tangent equations.

Tan(θ) = Opp/Adj

Tan(θ) = sin(θ)/cos(θ)

Tan(θ) = Adj/Opp

Tan(θ) = 1/sin(θ)

Tan(θ) = cos(θ)/sin(θ)

tan(θ) = Opp/Adj and also equals sin(θ)/cos(θ).

Explanation

tan(θ) = Opp/Adj and also equals sin(θ)/cos(θ).

Submit

15) The cosine of an angle is always greater than the sine for acute angles less than 45°.

True

False

True. For angles opposite, so cos(θ) > sin(θ).

Explanation

True. For angles opposite, so cos(θ) > sin(θ).

16) If sin(θ) = 0.6, find θ.

30°

36.87°

45°

60°

θ = sin⁻¹(0.6) = 36.87°. This matches a 3-4-5 triangle (3/5 = 0.6).

Explanation

θ = sin⁻¹(0.6) = 36.87°. This matches a 3-4-5 triangle (3/5 = 0.6).

17) Sine and cosine of complementary angles are equal.

True

False

True. sin(θ) = cos(90° - θ). Example: sin(30°) = cos(60°) = 0.5.

Explanation

True. sin(θ) = cos(90° - θ). Example: sin(30°) = cos(60°) = 0.5.

18) Tangent can be greater than 1.

True

False

True. tan(θ) > 1 when Opp > Adj. Example: tan(60°) = √3 ≈ 1.732.

Explanation

True. tan(θ) > 1 when Opp > Adj. Example: tan(60°) = √3 ≈ 1.732.

19) If cos(θ) = 0.8, find θ.

53.13°

45°

36.87°

60°

θ = cos⁻¹(0.8) = 36.87°

Explanation

θ = cos⁻¹(0.8) = 36.87°

20) Select all equations that represent cosine.

Cos(θ) = Adj/Hyp

Cos(θ) = sin(90° - θ)

Cos(θ) = 1/sin(θ)

Cos(θ) = Hyp/Adj

Cos(θ) = tan(θ)*sin(θ)

cos(θ) = Adj/Hyp and equals sin(90° - θ).

Explanation

cos(θ) = Adj/Hyp and equals sin(90° - θ).

Submit

SOHCAHTOA Quiz: Defining SOHCAHTOA

1) What does SOH in SOHCAHTOA stand for?

2)

What first name or nickname would you like us to use?

2) Select all correct SOHCAHTOA relationships.

3) What does CAH in SOHCAHTOA stand for?

4) The tangent of an angle is the ratio of the opposite side to the adjacent side.

5) The sine of an angle equals ______ divided by the hypotenuse.

6) The cosine of an angle equals ______ divided by the hypotenuse.

7) If cos(θ) = 12/13, what is sin(θ)?

8) If sin(θ) = 3/5, what is cos(θ)?

9) If sin(θ) = 4/5, what is tan(θ)?

10) If tan(θ) = 3/4, what is sin(θ)?

11) The tangent of an angle equals the opposite divided by the ______ side.

12) If sin(θ) = 5/13, find tan(θ).

13) If tan(θ) = 1, what is θ?

14) Choose all correct tangent equations.

15) The cosine of an angle is always greater than the sine for acute angles less than 45°.

16) If sin(θ) = 0.6, find θ.

17) Sine and cosine of complementary angles are equal.

18) Tangent can be greater than 1.

19) If cos(θ) = 0.8, find θ.

20) Select all equations that represent cosine.