Precalculus help --> cos2x=3/5 and 90<x<180

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In summary, The problem is to find the values of the 6 trig functions given that cos2(theta)=3/5, and theta is between 90 and 180 degrees. By using trig identities, we can determine that cos(theta)=-2/sqrt(5) and sin(theta)=1/sqrt(5), and use these values to find the remaining four trig functions.
  • #1
yeny
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Hello, can someone please help me with this problem?

I have to find the values of the 6 trig functions if the conditions provided hold

cos2(theta)=3/5

90 degrees is less than or equal to theta, and theta is also less than or equal to 180 degrees

THANK you so much.
 
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  • #2
yeny said:
Hello, can someone please help me with this problem?

I have to find the values of the 6 trig functions if the conditions provided hold

cos2(theta)=3/5

90 degrees is less than or equal to theta, and theta is also less than or equal to 180 degrees

given $\cos(2\theta) = \dfrac{3}{5}$ and $\theta$ resides in quadrant II ...

$\cos(2\theta) = 2\cos^2{\theta} -1 = \dfrac{3}{5} \implies \cos^2{\theta} = \dfrac{4}{5} \implies \cos{\theta} = - \dfrac{2}{\sqrt{5}}$

$\sin^2{\theta} = \dfrac{1}{5} \implies \sin{\theta} = \dfrac{1}{\sqrt{5}}$

use your basic trig identities to determine the values of the remaining four
 

FAQ: Precalculus help --> cos2x=3/5 and 90<x<180

1. What is the value of x if cos2x equals 3/5 and x is between 90 and 180 degrees?

The value of x would be approximately 48.2 degrees or 131.8 degrees. This is because cos2x is equal to 3/5 when x is equal to either 48.2 degrees or 131.8 degrees in the given range.

2. How do you solve for x in the equation cos2x=3/5?

To solve for x, you can use the inverse cosine function. In this case, you would take the inverse cosine of both sides of the equation, which would give you two solutions.

3. Can you graph the solution to cos2x=3/5 on the coordinate plane?

Yes, the solution can be graphed on the coordinate plane. Since cos2x is equal to 3/5 at two different values of x, there would be two points on the graph where the y-coordinate is equal to 3/5.

4. How does the value of x change if the given range is expanded to include negative values?

If the range is expanded to include negative values, the value of x would change to include negative values as well. This is because the cosine function is periodic, and as the range increases, the function repeats itself in the negative direction as well.

5. Is there a general formula for solving equations with trigonometric functions?

Yes, there are general formulas for solving equations with trigonometric functions such as the double-angle formula, half-angle formula, and sum and difference formulas. These formulas can be used to simplify and solve equations involving trigonometric functions.

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