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garik1379 [7]
2 years ago
14

part 2. Find the value of the trig function indicated, use for that Pythagorean theorem to find the third side if you need it.​

Mathematics
1 answer:
andreev551 [17]2 years ago
8 0

Answer:  \bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}

<u>Step-by-Step Explanation:</u>

Pythagorean Theorem is: a² + b² = c²  , <em>where "c" is the hypotenuse</em>

5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}

Note: (15)² + (3√11)² = hypotenuse²   →   hypotenuse = 18

6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}

Note: 8² + 15² = hypotenuse²   →   hypotenuse = 17

7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}

Note: hypotenuse not needed for tan

8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}

Note: 2² + 6² = hypotenuse²   →   hypotenuse = 2√10

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The equation according to the given verbal sentence is \frac{2 t+2}{2 s^{3}} (after solving this \frac{t+1}{s^{3}} ).

<u>Step-by-step explanation:</u>

Rewrite the given verbal sentence and so it will be easier to translate.

Given: The quotient of the sum of 2 t and 2 and twice the cube of s

sum of 2 t and 2 can be written as

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twice the cube of s

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Now, combine the above according to the given verbal. The quotient of the sum of 2 t and 2 and twice the cube of s  means,

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3 years ago
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3 years ago
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