In Exercises 1–6, use the figures to find the exact value of each...

Question

In Exercises 1–6, use the figures to find the exact value of each trigonometric function.

A right triangle labeled with sides 11, 60, and 61, and angle Δ, for trigonometric function exercises.

sin 2α

Accepted Answer

Hello, everyone. We are asked to determine the exact value of the trigonometric function. Using the provided figure, we are given a right triangle with an angle delta where the leg crossed from it is measures 11. The other leg measures 60 and the hypotenuse measures 61. We are trying to find the value of sign to delta. We have four answer choices to begin recall that if you have the sign of a double angle. So in this case, two delta, this is the double angle identity and this would be two sign delta cosine delta. So if we find what the sign of delta and the cosine of delta are, we can work with this to find the sign of two delta. So starting with the sign. So sign of delta, recall that sign is the leg that is opposite the angle divided by the hypo. So opposite delta is the value of 11 and the hypotenuse is 61. So the sign of delta is 11 61st cosine of delta will be the adjacent leg divided by the hypotenuse. So the adjacent leg has a value of 60. The hypotenuse is 61. So the cosine of delta is 60 divided by 61. So plugging this back into my identity, I have the sign of two delta equals two, multiplied by the sign of delta. So 11 60 firsts multiplied by the cosine of delta, which is 60 60 firsts. And when we multiply this straight across, we are left with 1320 as our numerator and 3721 as our denominator. So this is the exact value of the sign of two delta and that is answer choice. A have a nice day.

In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
sin 2α

Key Concepts

Trigonometric Functions

Double Angle Formulas

Pythagorean Theorem

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