Geometria- equações e relações fundametais

I have a Portuguese Water Dog who's translating for me.

a.

Usually I'll say the linear combination of a sine and a cosine of the same angle is a phase shift and a dilation etc. but here we can take a shortcut. The only time we'll get -1 as the sum is when one of the terms is -1, then the other term will be zero because of .

x = 3π/2 or x=π

b.

That's the biggest cliche of trig 30/60/90 so x=plus or minus 60 degrees. We're told we're in the fourth quadrant, so

-√3/2

c.

This time we're in the third quadrant, negative sine

-(1/4)√7

d.

Second quadrant positive sine, negative tangent

sin x = √7/5, tan x = -√14/6

e.

We're given the tangent and the sine

(-2/5)√5

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point