Given tanθ=sqrt(3). Determine the value of other trig functions.

TL;DR

This analysis explains how to find the trigonometric function values in quadrant 3 using the given tangent theta value of square root 3.

Transcript

okay we're given that tangent theta is equal to script 3 and we know that theta is in the quadrant 3 and we're trying to figure the rest of the trig function values right so that's C and this one study trickier so pay close attention to this let me first write down tenjin say that and the definition of tension data in the xy-plane years this is the... Read More

Key Insights

• ❣️ Selecting the correct values for x and y is crucial in determining the quadrant in which the angle resides.
• 🆘 The value of r can be calculated using the Pythagorean theorem, which helps in finding the trigonometric function values.
• 😑 Rationalizing the denominator may be necessary to simplify the trigonometric function values and express them in a more simplified form.
• 👨‍💼 Practicing and understanding the definitions of sine, cosine, tangent, cosecant, secant, and cotangent is essential in solving trigonometric problems.
• ⚾ The given content focuses on finding the trigonometric function values based on a given tangent theta value in quadrant 3.
• 🪈 The author emphasizes the significance of correctly interpreting the quadrant in order to determine the correct trigonometric function values.
• 🪈 The content also suggests the importance of practice in order to improve understanding and memory of trigonometric concepts.

Questions & Answers

Q: How does finding the correct values for x and y affect the quadrant in which the angle resides?

Finding the correct values for x and y ensures that the angle is in the correct quadrant. In this case, using x=-1 and y=-square root of 3 places the angle in quadrant 3.

Q: How can we determine the value of r (the radius) using the given x and y values?

The value of r can be determined by using the formula r=sqrt(x^2 + y^2). In this case, substituting x=-1 and y=-square root of 3 into the formula gives r=sqrt(1 + 3) = sqrt(4) = 2.

Q: What is the value of the sine of theta based on the given x, y, and r values?

The value of sine theta is found by dividing the y value by the r value. In this case, sin(theta) = (-square root of 3) / 2.

Q: How can we rationalize the denominator for the cotangent of theta?

To rationalize the denominator for the cotangent of theta, multiply both the numerator and the denominator by the conjugate of the denominator. In this case, we multiply the numerator and denominator by -square root of 3, resulting in cot(theta) = -1 / square root of 3.

Summary & Key Takeaways

• The content discusses finding the trigonometric function values in quadrant 3 based on a given tangent theta value of square root 3.

• The author initially suggests using x=1 and y=square root of 3, but realizes that this is incorrect as it does not satisfy the conditions for quadrant 3.

• The correct values for x and y in quadrant 3 are x=-1 and y=-square root of 3, which are used to determine the trigonometric function values.