How would you solve questions like these?

[Quack 1,568]

Im kinda confused about these:

 

Use a calculator to find all solutions. (Let k represent an arbitrary integer. Round your answers to four decimal places.)

sin(x) = −0.48

x= ________________ ±2πk   (solution with the terminal side of x in the third quadrant)

x= ________________ ±2πk   (solution with the terminal side of x in the fourth quadrant)

 

also one like this:

 

Use a calculator to find all solutions to four decimal places. (Let k represent an arbitrary integer. Round your answers to four decimal places.)

cos(x) = 0.77

x= _________________ ±2πk     (solution with the terminal side of x in the first quadrant)

x= _________________ ±2πk     (solution with the terminal side of x in the fourth quadrant)

[Shawnic 2,977]

It's easy. You know that trigonometric functions likes sine and cosine have periods of 2π, i.e. they repeat their values after 2π. so sin(x) = sin(2π +x) = sin (4π + x) = sin(2πk + x) where k is an integer. 

You know inverse trigonometry, right? If sin(x)  = -0.48, Using your calculator, find what principal value of x (value of x from -π to π) gives -0.48. In other words, find sin^-1 (-0.48) or arcsin(-0.48) 

[Emfoofoo 1,389]

i would give up and throw it away.

[Rob 705]

2 hours ago, Emfoofoo said:

i would give up and throw it away.

emfoofoo is my spirit animal

[Conan Edogawa 837]

16 hours ago, Emfoofoo said:

i would give up and throw it away.

What a useful, practical hint. /s

[Shawnic 2,977]

23 hours ago, Master Flap said:

It's easy. You know that trigonometric functions likes sine and cosine have periods of 2π, i.e. they repeat their values after 2π. so sin(x) = sin(2π +x) = sin (4π + x) = sin(2πk + x) where k is an integer. 

You know inverse trigonometry, right? If sin(x)  = -0.48, Using your calculator, find what principal value of x (value of x from -π to π) gives -0.48. In other words, find sin^-1 (-0.48) or arcsin(-0.48) 

@Quack Obviously this didn't help.  

[Grant 646]

As usual, @Master Flap comes in and saves the day.

[Quack 1,568]

7 hours ago, Master Flap said:

@Quack Obviously this didn't help.  

oh no, it did.

it just took my brain a little while to process

little longer than expected.

[Echo 746]

Not sure why people are getting confused, the answer is simply

Spoiler

42

 

[Quack 1,568]

16 hours ago, FOX545 said:

Not sure why people are getting confused, the answer is simply

  Hide contents

42

 

oh yas. 42 solves everything!