Trigonometry Test # 3

1. Period of a graph.

Period is equal to c in the equation y=asin(bx+c)+d.

Period is equal to a in the equation y=asin(bx+c)+d.

Period is equal to d in the equation y=asin(bx+c)+d.

When equation: y=asin(bx+c)+dNote: the fuction could be sine,cos,tan,csc,sec, and cotsine and cosine: 2pi/b--> and csc and sectangent: pi/b--> and cot

The correct answer explains the different periods for different trigonometric functions based on the given equation. The incorrect answers provide common misconceptions regarding the parameters in the equation, leading to misleading information about the period.

Explanation

The correct answer explains the different periods for different trigonometric functions based on the given equation. The incorrect answers provide common misconceptions regarding the parameters in the equation, leading to misleading information about the period.

2. What is the Phase Shift formula for a graph?

C. Phase shift= -b/c

For all equations: y=asin(orcos,tan...)(bx+c)+dPhase shift= -c/b

B. Phase shift= -a/c

A. Phase shift= -d/b

The correct formula for phase shift of a graph is determined by the parameter 'c' and 'b' within the trigonometric function portion of the equation in the form y=asin(bx+c)+d. By calculating -c/b, you can find the phase shift value.

Explanation

The correct formula for phase shift of a graph is determined by the parameter 'c' and 'b' within the trigonometric function portion of the equation in the form y=asin(bx+c)+d. By calculating -c/b, you can find the phase shift value.

3. How can you graph sine functions?

Some things to remember: - the zero's of a sin graph will always be: (pi/b,a) and (2pi/b, a) and (0,0) -->This is WITHOUT the PHASE SHIFT!!!!- A regular sin graph has a period of 2pi. Steps(for complex graph)in : y=asin(bx+c)+d1. determine the period using 2pi/b2. Using this value create 4 points on the x-axis3. Graph y=asinbx4.Determine the phase shift: -c/b and shift your graph5. Then move it d vertically. If d is positive, move it up, if negative, down. *You can use the zero values as help.*For absolute value's: just remember that everything will be above the x-axisFor negative graphs, remember everything will be flipped

Use a scatter plot for representation

Draw a straight line through the origin

Always start from the highest point on the graph

Sine graphs involve periodic oscillations and are characterized by specific properties such as zero points, phase shift, and amplitude adjustments based on the equation parameters.

Explanation

Sine graphs involve periodic oscillations and are characterized by specific properties such as zero points, phase shift, and amplitude adjustments based on the equation parameters.

4. What is a helpful tip to remember when graphing cosine functions?

The period of a cosine graph is always 4pi/b.

Some thing helpful to remember:The zero's for a cosine graph are (3pi/2b, a) and (pi/ 2b, a). This is WITHOUT PHASE SHIFTS!!!!- A regular cosine graph has a period of 2pi
Steps (for complex graphs):in: y=acos(bx+c)+d1. determine period: 2pi/b2. Divide period by 4 and label the 4 points on x-axis3.Using these points, graph y=acosbx4. Determine phase shift (-c/b) and shift graph5. Using d move it vertically, same principles as sin apply*Use zero values to help you*

The zero's for a sine graph are (3pi/2b, a) and (pi/2b, a).

Vertical shifting in a cosine graph does not depend on 'd' value.

Understanding the key concepts and steps to graphing cosine functions is essential for accurately plotting the graph. Remembering the correct zero values, period calculation, and vertical shifting process can greatly aid in graphing cosine functions correctly.

Explanation

Understanding the key concepts and steps to graphing cosine functions is essential for accurately plotting the graph. Remembering the correct zero values, period calculation, and vertical shifting process can greatly aid in graphing cosine functions correctly.

5. How to graph csc functions?

Create a straight line graph with any slope.

Graph the cosine graph of the equation.

The best way to graph a csc graph is to graph the sin graph of the same equation first. Then, the zeroes of this sine graph will be the asymtotes of the csc graph. Using the "Vertices" make a "U". Refer to Graphing sin funcions flashcard.

Start by graphing the tangent graph.

To graph csc functions, it is important to understand the relationship between csc and sin graphs, and how to identify asymptotes for the csc graph based on the sin graph. Simply graphing the cosine graph, a straight line, or the tangent graph will not result in an accurate csc graph.

Explanation

To graph csc functions, it is important to understand the relationship between csc and sin graphs, and how to identify asymptotes for the csc graph based on the sin graph. Simply graphing the cosine graph, a straight line, or the tangent graph will not result in an accurate csc graph.

6. How can we graph sec graphs?

Graph the sec graph as a simple sine wave.

Plot the sec graph directly without any prior reference.

The best way to graph a sec graph is to graph the cos graph of the same equation first. Then, the zeroes of this cosine graph will be the asymtotes of the sec graph. Using the "Vertices" make a "U". Refer to Graphing cosine funcions flashcard.

Utilize the tangent graph to determine the sec graph.

To graph sec graphs accurately, it is important to understand the relationship between sec and cos functions, and how to use the cosine graph to determine the asymptotes of the sec graph.

Explanation

To graph sec graphs accurately, it is important to understand the relationship between sec and cos functions, and how to use the cosine graph to determine the asymptotes of the sec graph.

7. How to graph cot graphs?

Zeroes:(pi/4b, a) and (3pi/4b, -a) WITHOUT phase shifts
Similar steps as tan, only graph is in other direction. Refer to tanx flashcard. Just remember cot x is 1/tanx

Zeroes:(pi/2b, a) and (3pi/2b, -a) WITH phase shifts, unlike tan graphs.

Zeroes:(pi/3b, a) and (4pi/3b, -a) WITHOUT any phase shifts, depicting a unique characteristic of cot graphs.

Zeroes:(pi/6b, a) and (5pi/6b, -a) WITH phase shifts. Differentiate between tan and cot graphs.

The correct answer provides the appropriate steps to graph cot graphs properly, emphasizing the relationship between cot and tan graphs. The incorrect answers present common misconceptions or errors that one may encounter when graphing cot functions, highlighting the importance of understanding key concepts.

Explanation

The correct answer provides the appropriate steps to graph cot graphs properly, emphasizing the relationship between cot and tan graphs. The incorrect answers present common misconceptions or errors that one may encounter when graphing cot functions, highlighting the importance of understanding key concepts.

8. What are Pythagorean identities?

C. Principles that dictate the behavior of electrons in a magnetic field.

B. Formulas used to calculate the area of a circle.

A. Equations used in algebraic geometry to solve for right triangles.

Pythagorean identities are specifically related to trigonometry and are based on the Pythagorean theorem, which is a fundamental concept in geometry.

Explanation

Pythagorean identities are specifically related to trigonometry and are based on the Pythagorean theorem, which is a fundamental concept in geometry.