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 = 51

Accepted Answer

Welcome back. I am so glad you're here. We're told using a calculator determine the approximate values of the sine of P and the cosine of P where angle P equals 47 identify in which quadrant, an angle of P radiance is located. Our answer choices are answer choice. A, the sign of 47 is approximately 0.1236. And the cosine of 47 is approximately 0.9923 quadrant one answer choice B the sine of 47 is approximately 0.1236. And the cosine of 47 is approximately negative 0.9923 quadrant two. Answer choice C, the sin of 47 is approximately negative 0.9923. And the cosine of 47 is approximately 0.1236 quadrant four. And answer choice D the sine of 47 is approximately 0.9923. And the cosine of 47 is approximately negative 0.1236 quadrant four. All right. So a couple different things we need to figure out. The first one though is we can just plug into our calculator. You want to first make sure that you are in radiance mode, not degrees in radiance mode and you just plug in sign, it'll give you a parentheses, put in 47 and the parentheses and you'll get something like 0.12357 and that keeps going. But all of our answers here rounded to the fourth decimal place and that's a 55 looks to the seven and rounds up. So we're talking about a sign of 47 being approximately 0.1236. Same thing for the cosine of 47 put that in and you'll get something like negative 0.99233 that keeps going rounding to the fourth decimal place. That's a three looks to the three remains a three. So the cosine of 47 is approximately negative 0.9923. So which quadrant are we in? If we draw a quick sketch of a coordinate plane, we have a vertical Y axis and a horizontal X axis. They come together the origin in the middle. The first quadrant is up into the right of the origin. Second quadrant is up into the left of the origin. The third quadrant is down into the left of the origin and the fourth quadrant is down into the right of the origin. So where is s equal to a positive value? And cosine is equal to a negative value we recall from previous lessons, we've got that mnemonic device where all that's 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, it tells us where our trigonometric functions are positive in the first quadrant. All of them are positive. The second quadrant sign and its reciprocal function are positive in the third quadrant tangent and its reciprocal function are positive. And in the fourth quadrant cosine and its reciprocal function are positive. Here, we're just looking at sine and cosine sine needs to be positive that occurs in the first quadrant where they're all positive. And the second quadrant where S is positive cosine needs to be negative. Well, cosine is positive in the 1st and 4th quadrants. So it's going to be negative in the 2nd and 3rd quadrants. So where is this true for both of them? That's going to be in the third quadrant. So here we are talking about, excuse me, I said third and I highlighted second, it's the second quadrant. So quadrant two, we look at our answer choices for a positive sign value of 0.1236 a negative cosine value of negative 0.9923 and quadrant two. And that 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 = 51

Key Concepts

Trigonometric Functions

Unit Circle

Quadrants of the Coordinate Plane

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