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3 years ago

Use the diagram to find each angle measure.Explanation added please.

Mathematics

1 answer:

castortr0y [4]3 years ago

3 0

4. 120° ~ vertical angles are congruent

5. 13° ~ vertical angles are congruent

6. 70° ~ supplementary angles

7. 115° ~ supplementary angles

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Help please!

Mamont248 [21]

Answer: see proof below

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

Use the Sum & Difference Identity: cos (A + B) = cos A · cos B - sin A · sin B

Recall the following from Unit Circle: cos (π/2) = 0, sin (π/2) = 1

cos (π) = -1, sin (π) = 0

Use the Quotient Identity: $\tan A=\dfrac{\sin A}{\cos A}$

<u>Proof LHS → RHS:</u>

$\text{LHS:}\qquad \qquad \dfrac{\cos \bigg(\dfrac{\pi}{2}+x\bigg)}{\cos \bigg(\pi +x\bigg)}$

$\text{Sum Difference:}\qquad \dfrac{\cos \dfrac{\pi}{2}\cdot \cos x-\sin \dfrac{\pi}{2}\cdot \sin x}{\cos \pi \cdot \cos x-\sin \pi \cdot \sin x}$

$\text{Unit Circle:}\qquad \qquad \dfrac{0\cdot \cos x-1\cdot \sin x}{-1\cdot \cos x-0\cdot \sin x}$

$=\dfrac{-\sin x}{-\cos x}$

Quotient: tan x

LHS = RHS $\checkmark$

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m_a_m_a [10]

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Rufina [12.5K]

Answer:

Step-by-step explanation:

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