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3 years ago

Let θ be an angle in quadrant IV such that sinθ = -2/5 . Find the exact values of secθ and tanθ.

1 answer:

8 0

If θ lies in the fourth quadrant, then sin(θ) < 0 and cos(θ) > 0. So we have from the Pythagorean identity,

sin²(θ) + cos²(θ) = 1 ==> cos(θ) = +√(1 - sin²(θ)) = √21/5

Then

sec(θ) = 1/cos(θ) = 5/√21

and

tan(θ) = sin(θ)/cos(θ) = (-2/5)/(√21/5) = -2/√21

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Need help for question 8 and 9. I need the equation that’s passes through the points!

dsp73

Answer:

Step-by-step explanation:

Question 8

Let the equation of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

y = mx + b

Here, m = slope and y-intercept = b

Since, m = $\frac{y_2-y_1}{x_2-x_1}$

For two points (1, 4) and (5, 8),

m = $\frac{8-4}{5-1}$

m = 1

Equation will be,

y = (1)x + b

y = x + b

Since, this line passes through (1, 4),

4 = 1 + b

b = 3

Therefore, equation of the line will be,

y = x + 3

Question 9

Let the equation is y = mx + b

m = $\frac{y_2-y_1}{x_2-x_1}$

For two points (2, 10) and (6, 4)

m = $\frac{10-4}{2-6}$

m = $-\frac{3}{2}$

By substituting the value of 'm' in the equation,

y = $-\frac{3}{2}x+b$

Since, this line passes through (2, 10)

10 = $-\frac{3}{2}(2)+b$

b = 10 + 2

b = 12

Therefore, equation of the line will be,

$y=-\frac{3}{2}x+12$

4 0

3 years ago

What are the solution(s) to the quadratic equation 50 – x2 = 0?

Dmitrij [34]

Answer:

x = ± $5\sqrt{2}$

Step-by-step explanation:

We have been given the quadratic equation;

$50-x^{2}=0$

The first step is to subtract 50 from both sides of the equation;

$50-x^{2}-50=0-50$

$-x^{2}=-50$

Multiplying both sides by -1 yields;

$x^{2}=50$

The final step is to obtain square roots on both sides;

$\sqrt{x^{2} }=\sqrt{50}\\x=+/-\sqrt{50}$

Therefore, x = ± $5\sqrt{2}$

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3 years ago

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Snezhnost [94]

Answer:

Step-by-step explanation:

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3 years ago

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allsm [11]

Answer:

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Step-by-step explanation:

fhhhhhhhgtrhrehr this is the right answer

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3 years ago

What is the slope of this line?

Dahasolnce [82]

Slope is rise over run. Go up 1 unit, right 4 units to get to the next point.
the slope is 1/4

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3 years ago

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