Reviewing Trigonometry for Quadrant II: Sinθ When Cosθ = -1/4

In summary, to find the value of sinθ when cosθ=-1/4 and θ is in Quadrant II, you can either draw a picture and remember the definition of cosine, or use the fundamental identity and take into account the quadrant to determine the sign. It might also be helpful to review the unit circle and right triangle trigonometry. Congratulations on your successful first midterm!
  • #1

Homework Statement

Question: Find the value of sinθ if cosθ=−1/4 and θ is in Quadrant II

I have not done TRIG in a long time. Given this question, what should I read over/review ? I don't remember how to solve these types of questions?

Homework Equations

The Attempt at a Solution

Not sure what kind of attempt I can do... I have to memorize the unit circle correct?

P.S. - Thanks to Mark an Sammy for recent help - Got 93% on my first of 3 midterms :)
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  • #2

Might be good to draw a picture and remember the definition of cos in terms of lengths of sides of a right triangle. That should get you going in the right direction.
  • #3

Drawing a picture as hotvette suggests is an excellent idea. Another way is to use the fundamental identity ##\sin^2\theta + \cos^2\theta = 1## to solve for the cosine. The quadrant will help you choose the sign.

1. What is Quadrant II in Trigonometry?

Quadrant II is the second quadrant in the Cartesian coordinate system, where the x-coordinate is negative and the y-coordinate is positive. In Trigonometry, it is the quadrant where sine (sinθ) and cosecant (cscθ) are positive, while cosine (cosθ) and tangent (tanθ) are negative.

2. What is the value of sinθ when cosθ = -1/4 in Quadrant II?

In Quadrant II, the value of sinθ is always positive. When cosθ = -1/4, we can use the Pythagorean identity (sin²θ + cos²θ = 1) to find the value of sinθ. In this case, sinθ = √(1 - (-1/4)²) = √(1 - 1/16) = √(15/16) = √15/4 = √15/2.

3. How do you find the reference angle in Quadrant II?

The reference angle in Quadrant II is the angle between the terminal side of the given angle and the x-axis. To find it, we can subtract the given angle from 180 degrees. For example, if the given angle is 135 degrees, the reference angle would be 180 - 135 = 45 degrees.

4. What is the relationship between sine and cosine in Quadrant II?

In Quadrant II, sine and cosine are complementary functions, meaning they add up to 90 degrees. This can also be expressed as sinθ = cos(90 - θ). In the case of cosθ = -1/4, sinθ = √15/2, and cos(90 - θ) = √15/2.

5. How do you determine the other trigonometric functions (tanθ, cotθ, secθ, cscθ) in Quadrant II?

In Quadrant II, tangent (tanθ) and cotangent (cotθ) are negative, while secant (secθ) and cosecant (cscθ) are positive. We can use the definitions of these functions (opposite/hypotenuse for sine and cosecant, adjacent/hypotenuse for cosine and secant, and opposite/adjacent for tangent and cotangent) to find their values. For example, if sinθ = √15/2 and cosθ = -1/4, we can find tanθ = sinθ/cosθ = -(√15/2) / (-1/4) = √15/8.

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