All Precalculus Resources
Example Questions
Example Question #2 : Understanding Angles In The Unit Circle
What is the reference angle for ?
To find the reference angle, subtract (1 trip around the unit circle) from the given angle until you reach an angle which is less than .
Example Question #22 : Graphs And Inverses Of Trigonometric Functions
What is ?
If you examine the unit circle, you'll see that that .
Example Question #1 : Using The Unit Circle
What is ?
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 #11 : Angles
Which one of these is positive in quadrant III?
Tangent
No trig functions
Sine
Cosine
All trig functions
Tangent
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 #1 : Understanding Coterminal Angles
Find a coterminal angle for .
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 #22 : Graphing The Sine And Cosine Functions
Which of the following angles is coterminal with ?
Each angle given in the other choices is coterminal with .
Each angle given in the other choices is coterminal with .
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 #1 : Trigonometry
What is ?
To get rid of , we take the or of both sides.
Example Question #2 : Trigonometry
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 #21 : Graphing The Sine And Cosine Functions
What is the amplitude of the following equation?
Based on the generic form , a is the amplitude. Thus, the amplitude is 4.
Example Question #24 : Graphing The Sine And Cosine 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.)
First we must set up our equation given the information.
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