Exact values of sin(1140), cos(1140), tan(1140), csc(1140), sec(1140), cot(1140)

TL;DR

Learn how to find the exact values of trigonometric functions for an angle of 1140 degrees using special right triangles.

Transcript

okay I'm going to show you guys how to find the exact values for all the trig functions from the angle is 1140 degrees a few things that you have to keep in mind first you have to know how to show the picture and second you have to know how to find the reference angle and that serious you have to know you're special right triangles alright so let's... Read More

Key Insights

• ✈️ The angle 1140 degrees can be visualized and analyzed on the XY plane.
• 🔺 Special right triangles, like the 30-60-90 triangle, can be used to find trigonometric function values for specific angles.
• 🥳 The ratios of side lengths in special right triangles provide the exact values for sine, cosine, tangent, cosecant, secant, and cotangent.
• 🔺 Finding the reference angle is crucial in determining the values for trigonometric functions.
• 🔺 The angle 1140 degrees can be expressed as a multiple of 360 degrees plus a reference angle.
• 🔺 The use of special right triangles is a helpful strategy for solving trigonometric problems involving non-standard angles.
• 🥳 It is important to understand the ratio of side lengths in special right triangles to accurately find the values of trigonometric functions.

Questions & Answers

Q: How do you find the reference angle for an angle of 1140 degrees?

To find the reference angle, subtract multiples of 360 degrees until you reach an angle between 0 and 360 degrees. In this case, subtract 1 revolution (360 degrees) from 1140 to get 780 degrees as the reference angle.

Q: Why do we use special right triangles for finding trig values?

Special right triangles, such as the 30-60-90 triangle, have consistent ratios between their side lengths. By using these ratios, we can determine the exact values of trigonometric functions for specific angles, like 60 degrees in this case.

Q: How do you find the value of sine for an angle of 1140 degrees?

To find sine, divide the length of the side opposite the angle by the length of the hypotenuse. In the 30-60-90 triangle, the side opposite the 60-degree angle is √3, and the hypotenuse is 2. Therefore, the sine of 1140 degrees is (√3/2).

Q: What is the value of cotangent for an angle of 1140 degrees?

Cotangent is the reciprocal of tangent. Since the tangent of 1140 degrees is √3, the cotangent would be the reciprocal of that, which is (√3/1).

Summary & Key Takeaways

• The video demonstrates how to find the values of trigonometric functions for an angle of 1140 degrees.

• To do this, you need to understand how to visualize the angle on the XY plane, find the reference angle, and utilize special right triangles.

• By using a 30-60-90 special right triangle, you can determine the values for sine, cosine, tangent, cosecant, secant, and cotangent.