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Mathematics, 22.06.2019 21:00 karmaxnagisa20

Options for the one with the drop down menu: sin^2(a)+cos^2(a)=1 tan^2(a)+1=sec^2(a) 1+cot^2(a)=csc^2(a)


Options for the one with the drop down menu: sin^2(a)+cos^2(a)=1 tan^2(a)+1=sec^2(a) 1+cot^2(a)=csc

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Answer from: nurikchan

Algebra 2b U7 L8 Trigonometric Identities

1.D

2.B

3.D

4.C

5.B

100%

Step-by-step explanation:

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Answer from: lindselu

tan²A +1 = sec²A; cotA = -(3√7/7); A = 311.41°

Step-by-step explanation:

secA = 4/3

sec²A = 16/9  

Use the identity tan²A +1 = sec²A

tan²A = sec²A - 1 = 16/9 - 1 = 7/9

cot²A = 1/tan²A = 9/7

We are in the fourth quadrant, so the cotangent is negative.

cotA = -√(9/7) = -3/√7 = -(3√7/7)

tan A = 1/cotA = -√7/3

A = -48.59° = 311.41°

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Answer from: victoralaquinez

The expression that represents  is

Step-by-step explanation:

The trigonometric equation given to us is

We take the cosine inverse of both sides to obtain,

Recall that, the composition of a function of x and its inverse produces x.

That is  or

Similarly,

This implies that,

The correct answer is C.

Step-by-step explanation:

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Answer from: kikipie8504
We know the following relationship:

csc(\theta)=\frac{1}{sin(\theta)}

The domain of a function are the inputs of the function, that is, a function f is a relation that assigns to each element x in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function csc(\theta) we can write its domain as follows:

1. Domain of validity for csc(\theta):

D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0 
 
When:

sin(\theta)=0?

when:

\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi

where k is an integer either positive or negative. That is:

sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...

To match this with the choices above, the answer is:

"All real numbers except multiples of \pi"


2. which identity is not used in the proof of the identity 1+cot^{2}(\theta)=csc^{2}(\theta):

This identity can proved as follows:

sin^2{\theta}+cos^{2}(\theta)=1 \ Dividing \ by \ sin^{2}(\theta) \\ \\ \therefore \frac{sin^2{\theta}}{sin^{2}(\theta)}+\frac{cos^{2}(\theta)}{sin^{2}(\theta)}=\frac{1}{sin^{2}(\theta)} \\ \\ \therefore 1+cot^{2}(\theta)=csc^{2}(\theta)

The identity that is not used is as established in the statement above:

"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)

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