I’m confused by my math teachers instructions. She wrote “Use your knowledge of the unit circle, peeking only if you must, to find each angle.” 1) cos 135. 2) sin (13pi/6). and 3) sec (pi/4)
- To find the value of this, notice that it is in the second quadrant; (the cosine is negative in the 2nd quad.)
180°-135°= 45° therefore evaluate -cos(45°)= -√2/2
On the unit circle, 135° has the coordinates of (-√2/2, √2/2) and the cosine value is equal to the x-coordinate; If you need to, draw a triangle to find this. A 45°-45°-90° triangle has the hyp=√2 and the sides= 1. Since it is in the 2nd quad, and cos(x)= x (adjacent) / hyp, you get -1/√2= -√2/2
- This is a co-terminal angle, meaning if you subtracted 360°, or 2π , from the angle you will get an angle at the same position.
13π/6-2π= 13π/6 - 12π/6= π/6 This angle is in the first quadrant.
To change it into degrees, multiply by 180°/π, and subtract 360°.
(13π/6) * (180°/π)= 2340/6 =390°. 390°-360°= 30°
So, what is sin(30°)? From the unit circle, the coordinates of 30°, or π/6, = (√3/2, 1/2), and since the sine is equal to the y-coordinate, you just pick off the y value. You could also draw a 30-60-90 triangle
sin(13π/6)= sin(π/6)= sin(30°)= 1/2
What is π/4? it is equal to 45°. This has the coordinates (√2/2, √2/2)
Since secant is equal to 1/cos, and that cos(45°)= √2/2, sec(45°)= 1/(√2/2)=√2