Ask question

Ask question

All categories

3 years ago

15

Express the following as a function of a single angle sin 20° cos 30° + cos 20° sin 30°

1 answer:

m_a_m_a [10]3 years ago

8 0

Answer:

Cos= 30•

Step-by-step explanation: Apex

You might be interested in

Please help asap!! Due today!

Elena-2011 [213]

Answer:

25 cm

Step-by-step explanation:

a^2 + b^2 = c^2

7^2 + 24^2 = c^2

49 + 576 = c^2

c^2 = 625

c = 25

Answer: 25 cm

5 0

2 years ago

Which values of x are point(s) of discontinuity for this function? Function x = –4 x = –2 x = 0 x = 2 x = 4

Nadya [2.5K]

Answer:

the answer is x=0 and x=2

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

You are a financial advisor whose client is concerned about losing his investment if a company goes out of business. Which of th

34kurt

Answer:

You should advise him to buy preferred stock.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the slope-intercept form for a line that passes through (4,3) and is parallel to x=0

nikitadnepr [17]

Answer:

x=4

Step-by-step explanation:

x=0 is an undefined slope(straight line vertically)

We need the line to pass through the point (4,3)

So, we just take the x coordinate from the equation and make it also have an undefined slope.

x = 4

6 0

3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

or

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

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

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

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

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

2 years ago