If the Point (-12, -5) lies on the Terminal Side of theta, find the Six Trig Function Values | Summary and Q&A

TL;DR

Learn how to find the six trig function values for a given angle using the x and y coordinates.

Key Insights

• 🔺 The value of r represents the distance between the origin and a point on the terminal side of an angle.
• ➗ The sine of an angle can be determined by dividing the y-coordinate by the value of r.
• 👨‍💼 The reciprocal of sine is cosecant, obtained by flipping the answer for sine.
• 🗂️ The cosine of an angle is found by dividing the x-coordinate by the value of r.
• 🐬 The reciprocal of cosine is secant, obtained by flipping the answer for cosine.
• ❣️ The tangent of an angle is calculated by dividing the y-coordinate by the x-coordinate.
• 🐬 The reciprocal of tangent is cotangent, obtained by flipping the answer for tangent.

Transcript

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Questions & Answers

Q: What is the initial step in finding the six trig function values for the given angle?

The first step is to find the value of r, which represents the distance between the origin and the given point on the angle. It can be calculated using the formula r = √(x² + y²).

Q: How is the sine of theta calculated in this problem?

The sine of theta can be calculated by dividing the y-coordinate (-5) by the value of r (13). So, the sine of theta is -5/13.

Q: What is the reciprocal of sine and how is it calculated?

The reciprocal of sine is cosecant. To find the cosecant of theta, you simply flip the answer for sine. In this case, it would be -13/5.

Q: How can the tangent of theta be determined?

The tangent of theta can be found by dividing the y-coordinate (-5) by the x-coordinate (-12). So, the tangent of theta is 5/12.

Summary & Key Takeaways

• The problem involves finding the six trig function values for a given angle, where one point on the angle is (-12, -5).

• The first step is to find the value of r, which represents the distance between the origin and the given point.

• The trig function values for the angle can be determined using the x and y coordinates along with the value of r.