# Thread: Are these correct? Part 2

1. ## Are these correct? Part 2

16) if sin x= 1/5 then csc x =?

17) sec x = 5/4 and value of tan x is positive what is sin x equal?

18) cot x = 3/4 and cos x is negative. sin x =?

19) cos x = -1/2 the value of of x can be in the form α*pi what is the value of α?

20) the value of tan x is $\displaystyle sqrt{3}$. sin x is positive what is sec x?

21) Evaluate: $\displaystyle tan (sin^{-1}(1/sqrt{2}))$

22)$\displaystyle tan (cot^{-1}(1/3))=?$

23) $\displaystyle sin (pi/4 + pi/6)$ can be expressed in the form $\displaystyle [sqrt{2}(sqrt{3}+1)]/y$. whats y?

24) $\displaystyle cos (pi/4 + pi/6)$ can be expressed in the form $\displaystyle [sqrt{2}(sqrt{3}-1)]/z$ whats z?

25) if $\displaystyle sin x = sqrt{3}/2$ and $\displaystyle tan x= - sqrt{3}$ the vaule of x can be written in the form $\displaystyle api$. whats a?

26) sin x = 1/4 and cos x > 0. cos x can be expressed in the form $\displaystyle sqrt{a}/4$what is the value of a?

27) sin x =1/4 and cos x>0. sin (2x) can be written in the form $\displaystyle sqrt{15}/a$ what is the value of a?

28) cos x= 1/3 and sin (x/2) > 0. The value of sin (x/2) can be written as $\displaystyle 1/sqrt{a}$. what is a?

29) evaluate: $\displaystyle 1/2 log_{1/4} 80 - 1/2 log_{1/4} 5$

2. Hello, yoman360!

You did even better this time!

You did so well on every other problem,
. . I assume you forgot to type your answer to #24.

$\displaystyle 24)\;\;\cos \left(\tfrac{\pi}{4} + \tfrac{\pi}{6}\right)$ can be expressed in the form $\displaystyle \frac{\sqrt{2}\left(\sqrt{3}-1\right)}{z}$ What is $\displaystyle z$?

$\displaystyle \text{We have: }\;\cos\left(\tfrac{\pi}{4}+\tfrac{\pi}{6}\right) \;=\;\underbrace{\cos\tfrac{\pi}{4}}_{\frac{\sqrt{ 2}}{2}} \underbrace{\cos\tfrac{\pi}{6}}_{\frac{\sqrt{3}}{2 }} - \underbrace{\sin\tfrac{\pi}{4}}_{\frac{\sqrt{2}}{2 }}\underbrace{\sin\tfrac{\pi}{6}}_{\frac{1}{2}}$

. . . . . . . . $\displaystyle = \;\frac{\sqrt{2}\sqrt{3} - \sqrt{2}}{4} \;=\;\frac{\sqrt{2}\left(\sqrt{3}-1\right)}{4}$