Thread: Help on Trig Questions.

1. Use a Sum or difference identity to find the exact value of sin285degrees

2. If tanX = -3/4 and 90<x<180, find cosX (the 90 and 180 are degrees)

3. If (tanX)(cscX) = 3, find value of cosX

4. If tanX= 3/4 and 180<X<270, find the exact value of sin2X

5. Find the value of tan(A+b) if cosA = 13/5, tanB = 3/4, and 0<A<90

Originally Posted by Joker

[1. Use a Sum or difference identity to find the exact value of sin285degrees

$\displaystyle \sin\left(285^{\circ}\right) = \sin\left(180^{\circ}+105^{\circ}\right) = -\sin\left(105^{\circ}\right) = -\sin\left(60^{\circ}+45^{\circ}\right)$

Expand that using the 'sum or difference' formula for sine.

2. If tanX = -3/4 and 90<x<180, find cosX (the 90 and 180 are degrees)

Pythagoras' theorem: If $\displaystyle \tan{x} = \frac{-3}{4}$, then $\displaystyle \cos{x} = \frac{4}{\sqrt{(-3)^2+(4)^2}} = $...

3. If (tanX)(cscX) = 3, find value of cosX

$\displaystyle {\tan{x}}{\csc{x}} = \frac{\sin{x}}{\cos{x}\sin{x}} = \frac{1}{\cos{x}}, $ so $\displaystyle \cos{x} = \cdots$

4. If tanX= 3/4 and 180<X<270, find the exact value of sin2X

Write $\displaystyle \tan{x}$ in terms of $\displaystyle \cos{x}$ and $\displaystyle \sin{x}$ and use the identity $\displaystyle \sin{2x} = 2\sin{x}\cos{x}$.

5. Find the value of tan(A+b) if cosA = 13/5, tanB = 3/4, and 0<A<90

Write $\displaystyle \tan\left(a+b\right) = \frac{\sin\left(a+b\right)}{\cos\left(a+b\right)}$, use the 'sum-difference' formulas on both the
numerator and the denominator, and write $\displaystyle \tan{b}$ in terms of sine and cosine.