Math Inverse Trig. problems?

Question

how would u find out these problems?
1. tan^-1 1

2. acr sin 0.6157

or

3. arc tan 0.3839

either one.

please help and please at least explain it step by step instead of just putting an answer.

Answer 1

1. This is an exact value question; you should know that tan 45° = 1, so arctan 1 is 45° or π/4 (radians).

For 2 and 3, since you're given a four-digit decimal it's not an exact value problem, so just use your calculator to get the answers. Depending on your calculator the modifier button you need may be called "inv", 'inverse" or "arc". You should get
arcsin 0.6157 = 38.00°
arctan 0.3839 = 21.00°.

Answer 2

1. tan^-1 1
Take an isosceles right triangle. The two legs of the right triangle are equal and thus the two acute angles are also equal. Thus they each = 45 degrees. Since the tangent is one leg divided by the other the tangent is one since the legs are equal. Thus arctan (1) = 45 degrees or 225 degrees.

2. arcsin 0.6157 = 38.003 degrees (I used calculator).
arcsin x = x + (1/2)(x^3/3) + (1/2)(3/4)(x^5/5) + ....

3. arc tan 0.3839 = 21.002 degrees
There is a series for arctan as well.

Answer 3

1. Ok, so the tangent is the sin of theta over the cos of theta.
When these two are eqivalent the ratio is unity. This only happens when the angle is 45 degrees, or pi/4 radians.

The rest of the calcualtions should be performed on a calculator. (scientific)

2. type .6157 and hit the sin^-1 button
3. type .3839 and hit tan^-1 button

Answer 4

Trigonometric functions calculate trigonometric value a base of angle. Inverse Trigonometric functions return angle, calculated a base of trigonometric value. tan^-1 and arctan both assign tan inverse function. as well as sin^-1 and arcsin both assign sin inverse function. tan^-1(1)=45°, arctan 0,3839=21°0´6.47" arcsin 0.6157=38°0´10.08"

Answer 5

Question 1
tan ^(-1) (1) = 45° or 225°
ie tan 45° = 1 and tan 225° = 1
Question 2
sin^(-1) 0.6157 = 38° or 142°
ie sin 38° = 0.6157 and sin 142° = 0.6157
Question 3
tan^(-1) 0.389 = 21.3° or 201 .3°
ie tan 21.3° = 0.389 and tan 201.3° = 0.389

Answer 6

2 sin²x - sin x - 1 = 0 ( 2 sin x + 1)(sin x - 1) = 0 sin x = - 1/2 , sin x = 1 x = 210⁰ , 330⁰ , 90⁰

Answer 7

1. x= tan^-1 1
x=arctan(1)

1=tan x

tan 45=1

x=pi/4