Question

Someone help on these

Answer 1

Problem 5

Start with the 30-60-90 triangle template

If you divide all values in that template by 2, then you'll get the diagram shown below.

Notice that the ratio of adjacent over hypotenuse leads to sqrt(3)/2

So that diagram shows that cos(30) = sqrt(3)/2

Answer: Choice A) 30 degrees

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Problem 6

Theta = 210 is between 180 and 270, which places the angle in quadrant Q3. This is in the southwest corner. In Q3, we have sine and cosine negative. They divide to make tangent positive

tan = sin/cos = negative/negative = positive

So tangent is positive in Q3

Answer: Choice C) tangent

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Problem 7

Cosine is an even function which means cos(-x) = cos(x) for all real numbers x.

So,

cos(170) = cos(-170)

Then we'll find a coterminal angle of -170 which involves adding on 360

-170+360 = 190

The angles -170 and 190 point in the exact same direction

This then means cos(170) = cos(-170) = cos(190)

Or in short, cos(170) = cos(190)

Answer: Choice A)  cos(190)