Find all Trigonometric Function Values of Theta if tan(theta) = -15/8 and Theta is in Quadrant 2

TL;DR

Find all trig function values of theta in quadrant two given that the tangent of theta is -15/8.

Transcript

in this problem we have to find all trig function values of theta given that the tangent of theta is equal to negative 15 over eight and theta is in quadrant two so there's a couple ways of doing this let's do it this way let's first start about thinking about the quadrant so quadrant two is here so in this quadrant we have that x is negative and w... Read More

Key Insights

• ☺️ Quadrant two has a negative x and positive y.
• 😑 Simplifying the tangent expression is crucial to determining x and y accurately.
• 😀 The value for r can be found using the pythagorean theorem.
• 🐬 The reciprocal of a trig function can be obtained by flipping its numerator and denominator.

Questions & Answers

Q: How can the quadrant of theta be determined in this problem?

The quadrant of theta can be determined by analyzing the signs of x and y. In quadrant two, x is negative and y is positive.

Q: Why does the expression for tangent need to be simplified before finding x and y?

Simplifying the expression is crucial because it ensures clarity in identifying the values for x and y. In this case, -15/8 is simplified as y = 15 and x = -8.

Q: How is the value for r calculated?

The value for r is found using the formula r = sqrt(x^2 + y^2). For theta in quadrant two, r equals sqrt(15^2 + (-8)^2), which simplifies to 17.

Q: How are the cotangent, cosecant, and secant values obtained?

The cotangent is the reciprocal of tangent, so it is -8/15. Cosecant is the reciprocal of sine, which yields 17/15. The secant is the reciprocal of cosine, resulting in -17/8.

Summary & Key Takeaways

• In quadrant two, x is negative and y is positive.

• The tangent of theta is y/x, which is -15/8.

• By finding the values for x, y, and r, all six trig function values of theta can be determined.