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3241004551 [841]
3 years ago
7

If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ?

Mathematics
2 answers:
KIM [24]3 years ago
8 0

Answer:

The answer is

sin(\theta)=-\frac{\sqrt{2}}{2}

tan(\theta)=-1

Step-by-step explanation:

we know that

tan(\theta)=\frac{sin(\theta)}{cos(\theta)}

sin^{2}(\theta)+cos^{2}(\theta)=1

In this problem we have

cos(\theta)=\frac{\sqrt{2}}{2}

\frac{3\pi}{2}

so

The angle \theta belong to the third or fourth quadrant

The value of sin(\theta) is negative

Step 1

Find the value of  sin(\theta)

Remember

sin^{2}(\theta)+cos^{2}(\theta)=1

we have

cos(\theta)=\frac{\sqrt{2}}{2}

substitute

sin^{2}(\theta)+(\frac{\sqrt{2}}{2})^{2}=1

sin^{2}(\theta)=1-\frac{1}{2}

sin^{2}(\theta)=\frac{1}{2}

sin(\theta)=-\frac{\sqrt{2}}{2} ------> remember that the value is negative

Step 2

Find the value of tan(\theta)

tan(\theta)=\frac{sin(\theta)}{cos(\theta)}

we have

sin(\theta)=-\frac{\sqrt{2}}{2}

cos(\theta)=\frac{\sqrt{2}}{2}

substitute

tan(\theta)=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}

tan(\theta)=-1

Ira Lisetskai [31]3 years ago
4 0
For the answer to the question above, <span>If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ? </span>

<span>If 3 pi over 2 < Θ < 2π Then the signs of sinx and tanx are both negative. </span>

<span>cos(x) = sqrt(2)/2. So sin(x) = -sqrt(2)/2 and tan(x) = -1. </span>

<span>sin Θ = square root 2 over 2; tan Θ = −1 </span>

<span>sin Θ = negative square root 2 over 2; tan Θ = 1 </span>

<span>sin Θ = square root 2 over 2; tan Θ = negative square root 2 </span>

<span>sin Θ = negative square root 2 over 2; tan Θ = −1</span>
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3 years ago
Two angles are supplementary. The measure of one angle is 4 times the measure of the other angle. What is the measure of the sma
Alexus [3.1K]
ANSWER

The smaller angle is

y = 36 \degree



.EXPLANATION

Let the angles be
x \:  and \:  \: y

where y is the smaller angle.
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This implies that,

x + y = 180 \degree...(1)


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x = 4y...(2)


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3 0
3 years ago
Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are
inna [77]
<span>a. The radius of earth is about 6400 kilometers. Find the circumference of a great circle.

Circumference = 2π(radius) = 2π(6400 km) = 40.212,39 km

b. Write an equation for the circumference of any latitude circle with angle theta

As stated, </span><span><span>the length of any parallel of latitude (this is the circumference of corresponding circle) is equal to the circumference of a great circle of Earth times the cosine of the latitude angle</span>:

=> Circumference = 2π*radius* cos(Θ) = 2 π*6400km*cos(Θ) = 40,212.39 cos(Θ)

Answer: circumference = 40,212.39 cos(Θ) km

c. Which latitude circle has a circumference of about 3593 kilometers?

Make </span><span><span>40,212.39 cos(Θ)</span> km = 3593 km

=> cos(Θ) = 3593 / 40,212.39 = 0.08935 => Θ = arccos(0.08935) = 84.5° = 1.48 rad

Answer: 1.48

d. What is the circumference of the Equator? </span>

For the Equator Θ = 0°

=> circumference = 40,213.49cos(0°) km = 40,212.49 km

Answer: 40,212.49 km

7 0
3 years ago
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