Question

How do you solve `cost-sin(2t)=0`?

Answer 1

`pi/6, pi/2, (5pi)/6, (3pi)/2`

Explanation:

Use trig identity:
sin 2t = 2sint.cos t
f(t) = cos t - 2sin t.cos t = cos t(1 - 2sin t) = 0
Use trig table and unit circle:
a. cos t = 0 --> arc `t = pi/2` and arc `t = (3pi)/2`
b. (1 - 2sin t) = 0
`sin t = 1/2`
Trig table and unit circle -->
arc `t = pi/6` and arc `t = pi - pi/6 = (5pi)/6`
Answers for `(0, 2pi)`:
`pi/6; pi/2, (5pi)/6, (3pi)/2`