The Terminal Side of Theta is given by 3x + 5y = 0, find the Six Trig Function Values of theta

TL;DR

Learn how to find the six trigonometric function values of a given angle using a provided equation.

Transcript

in this problem we're told that the terminal side of our angle theta is given by this equation here and we're being asked to find the six trig function values of theta so let's go ahead and work through this so we need to start by finding a point on this line so we can pick any value of x we like as long as it's positive it does say greater than or... Read More

Key Insights

• ☺️ Choosing strategic values for x can help eliminate fractions and simplify calculations.
• 😀 The formula r = √(x^2 + y^2) is used to find the value of r in trigonometry problems.
• 🥳 Sine, cosine, and tangent can be found using ratios of coordinates and the value of r.
• 🤙 The reciprocals of sine, cosine, and tangent are called cosecant, secant, and cotangent, respectively.

Questions & Answers

Q: How can I find a point on the line given in the problem?

You can choose any positive value for x, eliminating fractions. For example, picking x = 5 results in the point (5, -3).

Q: What is the formula for finding the value of r in trigonometry problems?

The formula is r = √(x^2 + y^2), where x and y are the cartesian coordinates of a point on the line.

Q: How can I find the sine of the angle?

The sine of the angle (θ) is calculated by dividing the y-coordinate by the value of r. In this case, it is -3/√34.

Q: What is the reciprocal of cosecant (csc)?

Cosecant is the reciprocal of sine. To find csc, you need to reciprocate the value obtained for sine. So, csc is -√34/3.

Q: How do I find cosine (cos) of the angle?

Cosine is found by dividing the x-coordinate by the value of r. In this problem, cos is equal to 5/√34.

Q: What is the reciprocal of secant (sec)?

Secant is the reciprocal of cosine. To find sec, reciprocate the value obtained for cosine. So, sec is √34/5.

Q: How can I calculate the tangent (tan) of the angle?

Tangent is found by dividing the y-coordinate by the x-coordinate. In this case, tan is -3/5.

Q: What is the reciprocal of tangent (cot)?

Cotangent is the reciprocal of tangent. To find cot, reciprocate the value obtained for tangent. Therefore, cot is -5/3.

Summary & Key Takeaways

• The problem requires finding the six trig function values of a given angle by solving an equation.

• To find a point on the line, choose a positive value for x that eliminates fractions.

• Use the formula r = √(x^2 + y^2) to find the value of r, where x and y are coordinates on the line.