Look at this table.

Cosθ=−2√3 , where π≤θ≤3π2 .

Alex787 [66]

Answer:

$sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}$

Step-by-step explanation:

step 1

Find the $sin(\theta)$

we know that

Applying the trigonometric identity

$sin^2(\theta)+ cos^2(\theta)=1$

we have

$cos(\theta)=-\frac{\sqrt{2}}{3}$

substitute

$sin^2(\theta)+ (-\frac{\sqrt{2}}{3})^2=1$

$sin^2(\theta)+ \frac{2}{9}=1$

$sin^2(\theta)=1- \frac{2}{9}$

$sin^2(\theta)= \frac{7}{9}$

$sin(\theta)=\pm\frac{\sqrt{7}}{3}$

Remember that

π≤θ≤3π/2

so

Angle θ belong to the III Quadrant

That means ----> The sin(θ) is negative

$sin(\theta)=-\frac{\sqrt{7}}{3}$

step 2

Find the sec(β)

Applying the trigonometric identity

$tan^2(\beta)+1= sec^2(\beta)$

we have

$tan(\beta)=\frac{4}{3}$

substitute

$(\frac{4}{3})^2+1= sec^2(\beta)$

$\frac{16}{9}+1= sec^2(\beta)$

$sec^2(\beta)=\frac{25}{9}$

$sec(\beta)=\pm\frac{5}{3}$

we know

0≤β≤π/2 ----> II Quadrant

so

sec(β), sin(β) and cos(β) are positive

$sec(\beta)=\frac{5}{3}$

Remember that

$sec(\beta)=\frac{1}{cos(\beta)}$

therefore

$cos(\beta)=\frac{3}{5}$

step 3

Find the sin(β)

we know that

$tan(\beta)=\frac{sin(\beta)}{cos(\beta)}$

we have

$tan(\beta)=\frac{4}{3}$

$cos(\beta)=\frac{3}{5}$

substitute

$(4/3)=\frac{sin(\beta)}{(3/5)}$

therefore

$sin(\beta)=\frac{4}{5}$

step 4

Find sin(θ+β)

we know that

$sin(A + B) = sin A cos B + cos A sin B$

so

In this problem

$sin(\theta + \beta) = sin(\theta)cos(\beta)+ cos(\theta)sin (\beta)$

we have

$sin(\theta)=-\frac{\sqrt{7}}{3}$

$cos(\theta)=-\frac{\sqrt{2}}{3}$

$sin(\beta)=\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute the given values in the formula

$sin(\theta + \beta) = (-\frac{\sqrt{7}}{3})(\frac{3}{5})+ (-\frac{\sqrt{2}}{3})(\frac{4}{5})$

$sin(\theta + \beta) = (-3\frac{\sqrt{7}}{15})+ (-4\frac{\sqrt{2}}{15})$

$sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}$

8 0

3 years ago

Fred purchased a boat for $8,645. He made a down payment of $775. He applied for a six-year installment loan with an interest ra

n200080 [17]

Answer:

135818564664 that the answer

6 0

3 years ago

Is 1/4 less than or greater than 1/8

lana66690 [7]

To find this answer, you need to find a common denominator. A common denominator is when the number on the bottom of two fractions is the same. The easiest was to do this is to first multiply the two denominators, then multiply the numerator (or top number) by the opposite denominator. This sounds complicated, but it's pretty simple. Here's the equation written out. (I hope this helps!)

4*8 = denominator for both numbers.

8*1 = numerator for the first number

4*1 = numerator for the second number.

This should give you the fractions with common denominators, 8/32 and 4/32. Then, to compare the fractions, just see which numerator is larger. In this case, 8 is larger than 1 which shows that 1/4 is greater than 1/8.

I hope this made sense. There's more than one way to solve these problems, so comment below if you would like me to explain it differently and I'll get back to you as soon as I can! :)

8 0

3 years ago

Read 2 more answers

When does the graph of a quadratic function open up?open down?

EastWind [94]

Answer:

1. >

2. <

Step-by-step explanation:

When a > 0, the graph opens upwards, or positively, because the way the line curves is determined by a.

When a < 0, the graph opens downwards, or negatively, for the same reason.

6 0

3 years ago

Which of the following will form the composite function G(F(x)) shown

photoshop1234 [79]

The answer is c F(x)= x2-5 and g(x)=c+4

6 0

3 years ago