Unit 4 - Objective 3 - Values of Trigonometric Functions


Signs of trigonometric functions in all four Quadrants.

u4obj301.gif (3591 bytes) u4obj302.gif (4067 bytes)
u4obj303.gif (3042 bytes)
u4obj304.gif (3064 bytes) u4obj305.gif (2936 bytes)

Reference Angles theta2.gif (141 bytes) are always next to the x-axis

Given the reference angle theta2.gif (141 bytes), you can find the angle theta.gif (128 bytes) in the appropriate quadrant and given angle theta.gif (128 bytes), you can find its reference angle.

1st Quadrant

u4obj308.gif (2244 bytes)

2nd Quadrant

u4obj309.gif (2044 bytes)

3rd Quadrant

u4obj310.gif (2192 bytes)

4th Quadrant

u4obj311.gif (2293 bytes)

The unit circle can be used to find trigonometric function for angles dividing the quadrants.

On the unit circle x^2 + y^2 = 1 and x = costheta.gif (128 bytes)
y = sintheta.gif (128 bytes)

 

Examples:

sin 90 = y = 1
cos 90 = x = 0
tan 90 = y/x = 1/0 = undefined

cot 90 = 1/tan 90 = x/y = 0/1 = 0
sec 90 = 1/cos 90 = 1/0 = undefined
csc 90 = 1/sin 90 = 1/1 = 1

u4obj312.gif (3173 bytes)

 

Special Triangles

u4obj313.gif (10691 bytes)

 

Examples:

1. Find the value for cos 150

u4obj316.gif (1295 bytes)

150 is in the 2nd quadrant, cos theta.gif (128 bytes) is negative in the 2nd quadrant, and the reference angle is

180 - 150 = 30
So cos 150 =
u4obj317.gif (213 bytes)


2. Find theta.gif (128 bytes) for tan theta.gif (128 bytes) = u4obj318.gif (168 bytes)

if 0 < or = theta.gif (128 bytes) < 360

The reference angle for tan theta.gif (128 bytes) = u4obj318.gif (168 bytes) is 30 and tan theta.gif (128 bytes) is positive in the 1st and 3rd quadrants so:

theta.gif (128 bytes) is 30, 180 + 30 = 210

 

 


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