Find all trig function values based on a given one, ex1

TL;DR

Explaining how to determine trigonometric ratios in Quadrant II using given information.

Transcript

okay we are given that tangent theta is equal to negative 15 over H and we know that theta is in the second quadrant right and based on this information we are going to figure this out well we not want answer already but anyways here is what were to show you let me write this down again we know tangent theta is equal to negative 15 over 8 right and... Read More

Key Insights

• 🥳 Understanding the sign of the tangent ratio helps identify the appropriate quadrant for the angle.
• 🥳 Determining correct x and y values is essential for calculating trigonometric ratios.
• 🥳 The hypotenuse (r) is crucial in finding sine, cosine, and tangent ratios in Quadrant II.
• 🤩 Utilizing the given information to create a right triangle representation is key in trigonometry.
• 🥳 Reciprocal trigonometric ratios can be easily calculated once the primary ratios are known.
• 🥺 Quadrant II in trigonometry involves negative x and positive y values, leading to specific calculations.
• 🔺 Trigonometric functions involve a relationship between angles, sides of a triangle, and ratios.

Questions & Answers

Q: How is the given information used to determine the quadrant for the angle in trigonometry?

The sign of the tangent ratio helps identify the quadrant, with negative tangents indicating Quadrant II and IV.

Q: How do you find the appropriate x and y values based on the given tangent ratio in Quadrant II?

By considering the signs of y and x, and choosing the correct pairing, y = -15 and x = -8 in Quadrant II.

Q: How is the hypotenuse (r) calculated in a right triangle in Quadrant II trigonometry?

The hypotenuse is calculated using the formula r = sqrt(x^2 + y^2), where x = -8, y = -15, resulting in r = 17.

Q: How do you determine sine, cosine, and tangent ratios using the calculated values in Quadrant II?

Sine theta = y/r, Cosine theta = x/r, Tangent theta = y/x are calculated as 15/17, -8/17, and -15/-8 respectively, in Quadrant II.

Summary & Key Takeaways

• Given tangent theta as -15/8, determining appropriate quadrant for the angle.

• Calculating y and x values based on the given tangent ratio.

• Utilizing y, x, and r to find sine, cosine, and tangent ratios in Quadrant II.