Trigonometric Equations

	-x	90°-x	90°+x	180°-x	180°+x	270°-x	270°+x	360°-x	360°+x
sin	-sin x	cos x	cos x	sin x	-sin x	-cos x	-cos x	-sin x	sin x
cos	cos x	sin x	-sin x	-cos x	-cos x	-sin x	sin x	cos x	cos x
Tan	-tan x	1/tan x	-1/tan x	-tan x	tan x	1/tan x	-1/tan x	-tan x	tan x

Remarks: 

When theta is 90° ± x or 270° ± x, sinàcos, cosàsin, tanà 1/tan. The sign is determined by the original sin/cos/tan in the given quadrant, assuming 0° ≤ x ≤ 90°.

For example: sin (90°+ x), assuming 0° ≤ x ≤ 90°

90°+ x should be in quadrant II and sin is positive in quadrant II.

So, sin (90°+ x) = +cos x

Actually, the answer can be easily checked just by randomly assigning a value for x and see whether sin (90°+ x) = +cos x

The following are some tricky questions.

Answer : A

Try to find out the pattern

Answer : B

To make a fraction smaller, we want the numerator(分子) smaller and the denominator(分母) greater. 

Also, recall sin x ranges from -1 to 1