# Precalculus

I am trying to submit this homework in but i guess i'm not doing it in exact values because it is not accepting it. I know i'm supposed to be using half angle formulas but maybe the quadrants are messing me up. Please help!

Find sin x/2 , cos x/2 , and tan x/2 from the given information. tan x = square root (15) , 0° < x < 90°

Find sin x/2 , cos x/2 , and tan x/2 from the given information.
cos x = (−12/13) 180° < x < 270°

1. 👍
2. 👎
3. 👁
1. if tanx = √15 or √15/1 , and x is in quad I
make a sketch of a right-angled triangle with opposite = √15
r^2 = (√15)^2 + 1^2 = 16
r = 4
then sinx = √15/4 and cosx = 1/4

if x is in quad I, then certainly x/2 is in quad I and everybody stays nicely positive

we know:
cosx = 1 - 2sin^2 (x/2)
1/4 = 1 - 2sin^2 (x/2)
2sin^2 (x/2) = 3/4
sin^2 x/2 = 3/8 = 6/16
sin (x/2) = √6/4
also sin^2 (x/2) + cos^2 (x/2) = 1
cos^2 (x/2) = 1 - 6/16 = 10/16
cos (x/2) = √10/4

also tan(x/2) = sin(x/2) / cos(x/2)
= (√6/4) / (√10/4)
= √6/√10
or √60/10 = 2√15/10 = √15/5

for the second, since x is in the third,
x/2 is in II
(e.g. if x = 182°, x = 91° ; if x = 278 , x/2 = 139°

given: cosx = - 12/13, other side is 5
sinx = -5/13

same as before ...
cos x = 1 - 2sin^2 (x/2)
-12/13 = 1 - 2sin^2 (x/2)
2sin^2 (x/2) = 1 + 12/13 = 25/13
sin^2 (x/2) = 25/26
sin (x/2) = ± 5/√26 , but x/2 is in II, so
sin (x/2) = 5/√26 or 5√26/26

again, as before:
sin^2 (x/2) + cos^2 (x/2) = 1
25/26 + cos^2(x/2) = 1
cos^2(x/2) = 1-25/26 = 1/26
cos(x/2) = ±1/√26, but in II cos(x/2) = -1/√26

finally, tan(x/2) = (5/√26) / (-1/√26) = -5

1. 👍
2. 👎

## Similar Questions

1. ### Math

Carol spends 1/2 hour doing math homework 4/5 hour doing science homework and 1/4 hour doing history homework about how much time did she spend in all doing her homework

2. ### 6.11.1 - Test: Adding and Subtracting Fractions Un

6.11.1 - Test: Adding and Subtracting Fractions Unit Test Part 1 Estimate the sum or difference. Use the benchmarks 0, one-half, and 1. one-half Carol spends one-half hour doing math homework, four-fifths hour doing science

3. ### English

Identify the correct sentence. A. I did my homework when the doorbell was ringing. B. I do my homework when the doorbell is ringing. C. I was doing my homework when the doorbell rang. D. I was doing my homework when the doorbell

4. ### finance

Suppose the spot rates for 1 and 2 years are s_1 = 6.3\%s 1 ​ =6.3% and s_2 = 6.9\%s 2 ​ =6.9% with annual compounding. Recall that in this course interest rates are always quoted on an annual basis unless otherwise specified.

1. ### finance

Suppose the borrowing rate r_B = 10\%r B ​ =10% compounded annually. However, the lending rate (or equivalently, the interest rate on deposits) is only 8\%8% compounded annually. Compute the difference between the upper and

2. ### Math Idk?

In a number guessing game. You ask a person to guess a number from one 1 to 10. If the person makes a random guess, what is the probability their guess will be less than 8?

3. ### english/poem

I am suppose to do a funny sonnet poem that has 10 syllables per line and 14 lines .Can you check my syllable or any mistakes. Oh homework! Oh homework! How I hate you! You smell, you stink, and you I don’t admire I want to tell

4. ### Math

There is a 60% that your math teacher will give a pop quiz tonight and, due to the fact that you have a soccer game, there is an 85% chance you will not be able to do your math homework. You decide that you will do the homework if

1. ### Math

On Tuesday, Leslie spent 47 minutes on math homework, 39 minutes on science homework, 52 minutes on English homework, and 44 minutes on history homework. How much time did Leslie spend doing her homework on Tuesday?

2. ### Math

Please explain in a more simple way, what I''m supposed to do? If you are unable to submit your answer to question 1 in audio form, you may submit your answer here. What are the steps to solve this problem? 0.000027 ÷ 0.000009

3. ### algebra

A contestant on a game show must guess the price of a new car. The contestant will win if his guess is within \$1000 of the price of the car. If the price of the car is \$24,995 and the contestant's guess is represented by g, what

4. ### Biology

1. Which of the following is a biotic factor that might affect the life of a water-dwelling organism? A. Temperature of the water B. Speed of water current C. Pollutions in water D. Bacterial population in water My guess: D? 2.