Ok im doing a problem and it includes finding the values of six trig functions...my question is if im given a angle [ 315 degrees ] and after finding the reference angle what numbers do i use? Do i use (checkmark 2 / 2 and checkmark 2 / 2??
Ok im doing a problem and it includes finding the values of six trig functions...my question is if im given a angle [ 315 degrees ] and after finding the reference angle what numbers do i use? Do i use (checkmark 2 / 2 and checkmark 2 / 2??
Given: $\displaystyle \theta = 315^{\text{o}}$
Take note that this angle is in the fourth quadrant. This means that the only the cosine/secant of this angle is positive.
First, find the reference angle.
$\displaystyle \theta_{ref} = 360 - 315 = 45^{\text{o}}$
Then, write down the six trigonometric functions of the original angle:
$\displaystyle \sin{315} = -\sin{45}$
$\displaystyle \cos{315} = \cos{45}$
$\displaystyle \tan{315} = -\tan{45}$
$\displaystyle \csc{315} = -\csc{45}$
$\displaystyle \sec{315} = \sec{45}$
$\displaystyle \cot{315} = -\cot{45}$
I will leave the evaluation for you.
Extra:
- If angle is in first quadrant, all trigonometric functions are positive
- If angle is in second quadrant, only sine/cosecant are positive
- If angle is in third quadrant, only tangent/cotangent are positive
- If angle is in fourth quadrant, only cosine/secant are positive
For angles 30, 45, and 60, you can use the special 45-45-90 and 30-60-90 triangles:
Special right triangles - Wikipedia, the free encyclopedia
To find the value of the trigonometric functions of these angles.