Question

Trig Help please! 50 points!

Answer 1

Coordinate geometry is one of the most important and exciting ideas of mathematics. In particular it is central to the mathematics students meet at school. It provides a connection between algebra and geometry through graphs of lines and curves. This enables geometric problems to be solved algebraically and provides geometric insights into algebra.

The invention of calculus was an extremely important development in mathematics that enabled mathematicians and physicists to model the real world in ways that was previously impossible. It brought together nearly all of algebra and geometry using the coordinate plane. The invention of calculus depended on the development of coordinate geometry.

Explanation:

Answer 2

C

Explanation:

Remember the mnemonic: SohCahToa, where:

`\sin(\theta)=\text{opposite}/\text{hypotenuse}\\\cos(\theta)=\text{adjacent}/\text{hypotenuse}\\\tan(\theta)=\text{opposite}/\text{adjacent}`

Let's determine our side lengths first.

Note that our angle is A. So, we have to determine the sides with respect to A.

The opposite side to A is 16.

The adjacent side is 12.

And the hypotenuse is 20.

With this, we can find our trig ratios:

Sine:

`\sin(A)=\text{opp}/\text{hyp}`

Substitute 16 for the opposite and 20 for the hypotenuse. This yields:

`\sin(A)=16/20`

Reduce:

`\sin(A)=4/5`

Cosine:

`\cos(A)=\text{adj}/\text{hyp}`

Substitute 12 for the adjacent and 20 for the hypotenuse. This yields:

`\cos(A)=12/20`

Reduce:

`\cos(A)=3/5`

Tangent:

`\tan(A)=\text{opp}/\text{adj}`

Substitute 16 for the opposite and 12 for the adjacent. This yields:

`\tan(A)=16/12`

Reduce:

`\tan(A)=4/3`

So, our answers are:

`(4)/(5), (3)/(5), \text{ and } (4)/(3)`

Out of the answer choices, the choice that represents this is C.

So, our correct answer is C.

And we're done!