Find the Six Trigonometric Function Values of Theta if (0, 5) lies on the Terminal Side of Theta

TL;DR

Calculate six trig function values for point (0, 5) on terminal side of angle theta – sin, cos, tan, csc, sec, cot.

Transcript

the point zero comma five lies on the terminal side of theta find these six trig function values of theta let's go ahead and work through this solution so zero five is gonna be like right here so here's the point 0 5 and then here's the angle so we're basically finding the six trig function values of pi over 2. now this type of problem is usually d... Read More

Key Insights

• ❣️ Understanding trig function values involves identifying x, y, and r components.
• ☺️ Tangent is undefined when x is zero.
• 🗂️ Secant is undefined when dividing by zero.
• 🐬 Reciprocal functions are found by flipping original values.

Questions & Answers

Q: How do you determine the value of r in this trigonometry problem?

To find the value of r, use the formula r = sqrt(x^2 + y^2). In this case, r = sqrt(0^2 + 5^2) = 5.

Q: Why is the tan value undefined in this scenario?

Tangent is calculated as y/x. Here, y = 5 and x = 0, which results in division by zero, making tan undefined.

Q: What are the reciprocal functions of sine, cosine, and tangent?

The reciprocals are cosecant (csc), secant (sec), and cotangent (cot) respectively, found by flipping the values – 1, undefined, and 0.

Q: How are the six trig function values determined in this problem?

The values are calculated using the formulas for sine, cosine, tangent, and their reciprocals after identifying x, y, and r values.

Summary & Key Takeaways

• Point (0, 5) lies on angle theta's terminal side.

• Find r = square root of (0^2 + 5^2) = 5.

• Trig function values: sin = 1, cos = 0, tan = undefined, csc = 1, sec = undefined, cot = 0.