For each value of s, use a calculator to find sin s and cos s,...

Question

For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which quadrant an angle of s radians lies.

s = 65

Accepted Answer

Welcome back. I am so glad you're here. We're told using a calculator determine the approximate values for the sine of P and the cosine of P where P equals 71 identify in which quadrant an angle of P radiance is located. Our answer choices are answer choice. A, the sign of 71 is approximately 0.9511. And the cosine of 71 is approximately negative 0.3090 quadrant one answer choice B the sign of 71 is approximately 0.9511. And the cosine of 71 is approximately negative 0.3090 quadrant two. Answer choice C. The sign of 71 is approximately negative 0.9511. And the cosine of 71 is approximately 0.3090 quadrant four and answer twist D. The sign of 71 is approximately negative 0.3090. And the cosine of 71 is approximately 0.9511 quadrant four. All right. So we've got a couple of different things to figure out. But the first one, we can start off just using our calculator. You want to make sure that you are in radiance mode, not degrees mode but radiance mode. Then you can just punch in the sign of it'll give you a parentheses you put in 71 and the parentheses hit enter and you'll get something like 0.95105 and that keeps going. But all of our answers here are rounded to the fourth decimal place here. That's a zero. It looks to the five and it rounds up. So that would be 0.9511. Same thing with cosine, cosine. It'll give you a parentheses. Put in 71 close the parenthesis hit, enter, you'll get something like negative 0.30902. It keeps going rounding to the fourth decimal place. That's again, a zero looks to the two and remains a zero. So this one is zero point. No, I'm looking at the wrong line. This one is negative 0.3090. So there's our sine and cosine values. But which quadrant are we in? Well, we can draw a rough sketch of a coordinate plane. We've got a vertical Y axis and a horizontal X axis. They come together at the origin in the middle up into the right of the origin is quadrant one up into the left of the origin is quadrant two, down into the left of the origin is quadrant three and down into the right of the origin is quadrant four. And we can recall the mnemonic device from previous lessons that all a in the first quadrant students, that's an S in the second quadrant take that's A T in the third quadrant calculus. That's ac in the fourth quadrant. And that tells us where all of the trigonometric functions are positive in quadrant one, all of the trigonometric functions are positive in quadrant two sine and its reciprocal function are positive in quadrant three tangent and its reciprocal function are positive. And in quadrant four cosine and its reciprocal function are positive. Here, we've got a sine value that's positive and we've got a cosine value that's negative. So where is sine positive and cosine negative? Well, sine is going to be positive where all trigonometric functions are positive in the first quadrant and in the second quadrant cosine is going to be negative. Well, it's positive in the 1st and 4th quadrants. So it's negative in the 2nd and 3rd quadrants. So where is it true for both of these? Where is sine positive and cosine negative? That's going to be in the second quadrant where both conditions are met. So we've got quadrant two for part of our answer. And we're told that the sign of 71 is a positive 0.9511 and the cosine of 71 is a negative 0.3090. This matches with answer choice B well, done. We'll catch you on the next one.

For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which quadrant an angle of s radians lies.
s = 65

Key Concepts

Unit Circle and Angle Measurement in Radians

Sine and Cosine Values and Their Signs

Quadrant Determination Using Trigonometric Signs

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