Question

1) iven sinx=45 and cosx=35 .

What is ratio for ​ tanx ​ ?


4)What is the value of x?


sin(x+22)°=cos(2x−7)°


Enter your answer in the box.


x =





Enter your answer in the boxes as a fraction in simplest form.


2)∠A is an acute angle in a right triangle.




Given that cosA=1517, what is the ratio for sinA?




Enter your answer in the boxes as a fraction in simplest form


3)Given sinx=0.5 , what is cosx ?




Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.


4)What is the value of x?


sin(x+22)°=cos(2x−7)°


Enter your answer in the box.


x =

Answer 1

Part 1)
`tan(x)=(4)/(3)`

Part 2)
`sin(A)=(8/17)`

Part 3)
`sin(x)=0.87`

Part 4)
`x=25\°`

Explanation:

Part 1) Note In this problem sinx should be 4/5 not 45 and cosx should be 3/5 not 35

Given sinx=4/5 and cosx=3/5 (see the note)

What is ratio for ​ tanx ​ ?

we know that

`tan(x)=(sin(x))/(cos(x))`

substitute the values

`tan(x)=((4/5))/((3/5))`

`tan(x)=(4)/(3)`

Part 2) ∠A is an acute angle in a right triangle

Note In this problem cosA should be 15/17 not 1517

Given that cosA=15/17, what is the ratio for sinA?

we know that

`sin^(2)(A)+cos^(2)(A)=1`

substitute the value of cos(A) and solve for sin(A)

`sin^(2)(A)+(15/17)^(2)=1`

`sin^(2)(A)=1-(225/289)`

`sin^(2)(A)=(64/289)`

`sin(A)=(8/17)`

Part 3) Given sinx=0.5 , what is cosx ?

we know that

`sin^(2)(x)+cos^(2)(x)=1`

substitute the value of sin(x) and solve for cos(x)

`sin^(2)(x)+(0.5)^(2)=1`

`sin^(2)(x)=1-0.25`

`sin^(2)(x)=0.75`

`sin(x)=0.87`

Part 4) What is the value of x?

sin(x+22)°=cos(2x−7)°

we know that

if
`sin(A)=cos(B)`

then

`A+B=90\°` -----> by complementary angles

so

in this problem

`(x+22)+(2x-7)=90\°`

solve for x

`3x+15\°=90\°`

`3x=90\°-15\°`

`x=75\°/3=25\°`