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Tema [17]
3 years ago
15

I don’t know where to start with this problem

Mathematics
1 answer:
elixir [45]3 years ago
4 0

Answer:

√(4/5)

Step-by-step explanation:

First, let's use reflection property to find tan θ.

tan(-θ) = 1/2

-tan θ = 1/2

tan θ = -1/2

Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.

Now let's look at the problem we need to solve:

sin(5π/2 + θ)

Use angle sum formula:

sin(5π/2) cos θ + sin θ cos(5π/2)

Sine and cosine have periods of 2π, so:

sin(π/2) cos θ + sin θ cos(π/2)

Evaluate:

(1) cos θ + sin θ (0)

cos θ

We need to write this in terms of tan θ.  We can use Pythagorean identity:

1 + tan² θ = sec² θ

1 + tan² θ = (1 / cos θ)²

±√(1 + tan² θ) = 1 / cos θ

cos θ = ±1 / √(1 + tan² θ)

Plugging in:

cos θ = ±1 / √(1 + (-1/2)²)

cos θ = ±1 / √(1 + 1/4)

cos θ = ±1 / √(5/4)

cos θ = ±√(4/5)

Since θ is in the fourth quadrant, cos θ > 0.  So:

cos θ = √(4/5)

Or, written in proper form:

cos θ = (2√5) / 5

You might be interested in
Using polygon STUVW what is m angle U ?
bija089 [108]

Answer:

The m∠ U is 72°.

Step-by-step explanation:

Given:

\angle S = 90\\\angle T = 2x\\\angle U = x\\\angle V = 2x\\\angle W = 90\\

To find :

\angle U = x = ?

Solution:

The sum of the measures of the interior angles of a polygon with 'n' sides is given as

\textrm{sum of the measures of angle of a polygon with 'n' sides} = (n - 1)\times 180

Here we have n = 5 on substituting the values we get

\angle S +\angle T + \angle U +\angle V + \angle W = (5 -2)\times 180\\90 + 2x + x + 2x + 90 = 3\times 180\\5x + 180 = 540\\5x = 540-180\\5x = 360\\x = \frac{360}{5}\\x = 72

Therefore,

m∠ U is 72°.

4 0
3 years ago
If f(x)=3x-2,find f(8)-f(-5)
Alexandra [31]

To find both f(8) and f(-5), we will need to plug in their values for x and solve for each. Then, we can subtract them to find the final answer.

Finding f(8):

f(8) = 3(8) - 2

f(8) = 24 - 2

f(8) = 22

Finding f(-5):

f(-5) = 3(-5) - 2

f(-5) = -15 - 2

f(-5) = -17

Subtracting f(8) and f(-5):

f(8) - f(-5)

22 - - 17

22 + 17

39

Hope this helps!! :)

6 0
3 years ago
3x - 3y = -15<br> -x + y = 5
Katyanochek1 [597]

Answer:

I don't understand what you're asking. can you put a question on this?

4 0
3 years ago
What is 0.24 numbers in two equivalent forms
zheka24 [161]
24/100 and 6/25 is are some of the equivalent form
8 0
3 years ago
Please help!!!!
Svet_ta [14]
5 would be the best answer choice
3 0
3 years ago
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