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3 years ago

Evaluate each trigonometric equation for θ.

Mathematics

1 answer:

liberstina [14]3 years ago

4 0

Answer:

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

Step-by-step explanation:

Let us revise the trigonometry functions

Sin(x) = opposite/hypotenuse

Cos(x) = adjacent/hypoteouse

Tan(x) = opposite/adjacent

Csc(x) = hypotenuse/opposit

Sec(x) = hypotenues/adjacent

Cot(x) = adjacent/opposite

In the given figure

The opposite side to angle Ф = 8

The adjacent side to angle Ф = 15

Find the hypotenuse using Pythagoras' theorem

$Hypotenuse = \sqrt{8^{2}+15^{2} }$

$Hypotenuse = \sqrt{64+225}$

$Hypotenuse = \sqrt{289}$

$Hypotenuse = 17$

Let us use the rules above to find the trigonometry functions

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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sveticcg [70]

a. Central angle in the circle is: Angle BAC

b. A major arc is: Arc BEC

c. A minor arc is: Arc BC

d. m(arc BEC) = 260°.

e. m(arc BC) = 100°.

<h3>What is the Central Angle Theorem?</h3>

The central angle theorem states that: the central angle measure of a circle equals the measure of the intercepted arc.

<h3>What is a Central Angle?</h3>

A central angle is formed by two radii of a circle, and the vertex of the angle is at the center of the circle.

<h3>What is a Major Arc?</h3>

Any arc that is more than half a circle (semicircle) or has a measure that is greater than 180 degrees, is referred to as a major arc of that circle. The measure of the major arc > 180 degrees.

<h3>What is a Minor Arc?</h3>

Any arc that is not more than half a circle (semicircle) or has a measure that is less than 180 degrees, is referred to as a minor arc of that circle. The measure of the minor arc < 180 degrees.

a. One central angle that can be identified in circle A is: Angle BAC

b. A major arc that can be identified in circle A is: Arc BEC

c. A minor arc that can be identified in circle A is: Arc BC.

d. According to the central angle theorem, we have:

m(arc BEC) = 360 - 100

m(arc BEC) = 260°

e. We are given that m(angle BAC) = 100°, therefore, according to the central angle theorem, we have:

m(arc BC) = m(angle BAC )

m(arc BC) = 100°

Learn more about major and minor arcs on:

brainly.com/question/16289520

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1 year ago

Evaluate sin(150∘) without using a calculator

Finger [1]

Answer:

1/2 or 0.5

Step-by-step explanation:

$sin(150 \degree) \\ = sin(180 \degree - 30 \degree) \\ = sin( 30 \degree) \\ = \frac{1}{2} \\ = 0.5 \\ \huge \red{ \boxed{sin(150 \degree) = 0.5}}$

8 0

3 years ago

Read 2 more answers

Find the value of the trigonometric ratio. Simplify the ratio of possible.(Hint:you may need to use pythagorean theorem first)

sergey [27]

Your answer will be 17/15

Firstly you should use Pythagorean’s theorem like this
H²=p²+b²
Where p is bc
And b is ac
Then keep the value and solve it and you will get h as 17
At last keep cosA = b/ h
Hope it helps : )
If you didn’t understand please tell me

4 0

3 years ago