Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #23 : Graphs And Inverses Of Trigonometric Functions

What is ?

Possible Answers:

Correct answer:

Explanation:

If you examine the unit circle, you'll see that the value of . You can also get this by examining a cosine graph and you'll see it crosses the point .

Example Question #24 : Graphs And Inverses Of Trigonometric Functions

Which one of these is positive in quadrant III?

Possible Answers:

Sine

No trig functions

Tangent

All trig functions

Cosine

Correct answer:

Tangent

Explanation:

The pattern for positive functions is All Student Take Calculus. In quandrant I, all trigonometric functions are positive. In quadrant II, sine is positive. In qudrant III, tangent is positive. In quadrant IV, cosine is positive.

Example Question #25 : Graphs And Inverses Of Trigonometric Functions

Find a coterminal angle for 

Possible Answers:

Correct answer:

Explanation:

Coterminal angles are angles that, when drawn in the standard position, share a terminal side. You can find these angles by adding or subtracting 360 to the given angle. Thus, the only angle measurement that works from the answers given is 

Example Question #26 : Graphs And Inverses Of Trigonometric Functions

Which of the following angles is coterminal with  ?

Possible Answers:

Each angle given in the other choices is coterminal with .

Correct answer:

Each angle given in the other choices is coterminal with .

Explanation:

For an angle to be coterminal with , that angle must be of the form  for some integer  - or, equivalently, the difference of the angle measures multiplied by must be an integer. We apply this test to all four choices.

 

:

 

:

 

:

 

:

 

All four choices pass the test, so all four angles are coterminal with .

Example Question #27 : Graphs And Inverses Of Trigonometric Functions

What is ?

Possible Answers:

Correct answer:

Explanation:

To get rid of , we take the or of both sides.

Example Question #1 : Trigonometric Operations

Trig_id

 

Possible Answers:

Correct answer:

Explanation:

In order to find  we need to utilize the given information in the problem.  We are given the opposite and hypotenuse sides.  We can then, by definition, find the  of  and its measure in degrees by utilizing the  function.

Now to find the measure of the angle using the  function.

If you calculated the angle's measure to be  then your calculator was set to radians and needs to be set on degrees.

Example Question #29 : Graphs And Inverses Of Trigonometric Functions

What is the amplitude of the following equation?

Possible Answers:

Correct answer:

Explanation:

Based on the generic form , a is the amplitude. Thus, the amplitude is 4.

Example Question #30 : Graphs And Inverses Of Trigonometric Functions

What is one possible length of side  if right triangle  has   and side  ?

 (Hint: There are two possible answers, but only one of them is listed.)

Possible Answers:

Correct answer:

Explanation:

First we must set up our equation given the information.

Example Question #81 : Pre Calculus

How many -intercepts does the function  have in the domain ?

Possible Answers:

Correct answer:

Explanation:

The period of the sine function is .  The period of our new function is 1.  Each period will have two zeroes and there will be one tacked on at the end when the domain is closed.  There will be -intercepts at

 

The graph is below.

 Wolframalpha--graph_of_y__sin2pix_from_x0_to_x5--2014-12-18_2321

Example Question #82 : Pre Calculus

If  and , then which of the following must be true about ?

Possible Answers:

Correct answer:

Explanation:

It is a question of what quadrant is in.

A negative value for secant indicates quadrant II or III. Since secant is the reciprocal of cosine, the measurement includes the x value and the r value with regards to position.To get a negative value for secant or cosine we will need a negative x value and either a positive or negative y value to get the correct r value.

A positive value for cotangent indicates quadrant I or III. Since cotangent is the reciprocal of tangent, the measurement includes the x and y values with regards to the position. To get a cotangent that is positive we will need a positive x value and either a positive or negative y value.

The overlap between these two statements is quadrant III. Therefore, must be in quadrant III.

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