# Thread: Are these correct? Part 2

1. ## Are these correct? Part 2

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

17) sec x = 5/4 and value of tan x is positive what is sin x equal?
my answer: 3/5

18) cot x = 3/4 and cos x is negative. sin x =?
my answer: -4/5

19) cos x = -1/2 the value of of x can be in the form α*pi what is the value of α?
my answer: 2/3

20) the value of tan x is $sqrt{3}$. sin x is positive what is sec x?
my answer: 2

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

22) $tan (cot^{-1}(1/3))=?$
My answer: 3

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

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

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

26) sin x = 1/4 and cos x > 0. cos x can be expressed in the form $sqrt{a}/4$what is the value of a?
my answer: 15

27) sin x =1/4 and cos x>0. sin (2x) can be written in the form $sqrt{15}/a$ what is the value of a?
My answer: 8

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

29) evaluate: $1/2 log_{1/4} 80 - 1/2 log_{1/4} 5$
my answer: -1

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.

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

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

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

Answer: 4

3. Thank you very much!