Find the Six Trig Function Values of Theta if cos(theta) = -3/5 and Theta is in Quadrant 3

TL;DR

Finding six trig function values based on cosine value in quadrant three.

Transcript

in this problem we have to find the six trig function values of theta and we're told that the cosine of theta is equal to negative three over five and we're also told that theta is in quadrant three so there's a couple ways of doing this problem we're going to start by focusing on the quadrant so let's draw a quick picture of the xy plane so this i... Read More

Key Insights

• ❣️ Understanding quadrant placement is crucial for determining signs of x and y values.
• ☺️ Using the cosine formula helps in finding x value when given the cosine of theta.
• 🗯️ Pythagorean theorem is useful in finding the missing side length in a right triangle.
• ❣️ Trigonometric functions can be calculated based on the x, y, and r values in a given quadrant.

Questions & Answers

Q: How do you determine the values of x and y in a quadrant based on the cosine value of theta?

To find x and y in a quadrant based on the cosine value of theta, use the cosine formula x = -3 and r = 5, then apply Pythagorean theorem to find y = -4.

Q: What are the steps to find the six trig function values of theta given x, y, and r values?

After determining x = -3, y = -4, and r = 5, calculate sine, cosine, tangent, cosecant, secant, and cotangent using the appropriate trigonometric formulas.

Summary & Key Takeaways

• Given cosine value of theta as -3/5 in quadrant three, determine x and y values.

• Using r = 5, x = -3, find y using Pythagorean theorem, resulting in y = -4.

• Calculate sine, cosine, tangent, cosecant, secant, cotangent of theta using x, y, and r values.