For an angle θ with the point (16, −30) on its terminating side, what is the value of cosine?

Asked by maham237 @ in Mathematics viewed by 309 People

For an angle θ with the point (16, −30) on its terminating side, what is the value of cosine?

Answered by maham237 @


First, let's locate the point's position in the x-y coordinate. Since x is positive and y is negative, we can place the point in the fourth quadrant. You may check the image so the next steps will be clearer as well.

Seeing that the legs of the right triangle formed are 16 and 30, we can apply the Pythagorean theorem to solve for the triangle's hypotenuse. Hence, we have

hypotenuse = √(16² + 30²) = 34

Recall that the cosine of a triangle's angle is the value of the ratio of the side adjacent to the angle and the triangle's hypotenuse. Or simply, we have

\cos\theta = \frac{A}{H}
\cos\theta = \frac{-30}{34}
\cos\theta = \frac{-15}{17}

Answer: -15/17



Similar Questions

For an angle θ with the point (12, −5) on its terminating side, what is the value of cosine?

Asked by maham237 @ in Mathematics viewed by 397 persons

For an angle θ with the point (5, -12) on its terminating side, what is the value of cosine?

Asked by maham237 @ in Mathematics viewed by 319 persons

Choose the point on the terminal side of -45°.

Asked by maham237 @ in Mathematics viewed by 243 persons

Choose the point on the terminal side of -210°.

Choose the point on the terminal side of 135°.

Asked by maham237 @ in Mathematics viewed by 248 persons

A. (-1, sqrt 3) B. (-sqrt 3, 1) C. (-1, 1) D. (sqrt 3, -1)

Take any three non-collinear points a b c and draw triangle a,b,c. through each vertex of the triangle draw a line parallel to the opposite side using ruler and compass

Asked by wiki @ in Mathematics viewed by 1487 persons

Which can be a possible next step in the construction of an angle with a side on line l that is congruent to abc? a. use a straightedge to draw a line that passes through point b and intersects line l. b. plot a point on ba. c. plot a point on line l. d. plot a point on bc.

Asked by maham237 @ in Mathematics viewed by 355 persons

In the following figure, what is the value of the potential at points a and b?

Asked by maham237 @ in Physics viewed by 327 persons

In the following figure, what is the value of the potential at points a and b? (Figure 1) picture a square.There is a 15 v battery on the left side, …

An acute angle θ is in a right triangle with sin θ = . what is the value of cot θ?

Asked by maham237 @ in Mathematics viewed by 275 persons

Which of the following are right triangle congruence theorems? check all that apply. a. hypotenuse-angle (ha) b. hypotenuse-leg (hl) c. leg-leg (ll) d. leg-angle (la

Asked by maham237 @ in Mathematics viewed by 421 persons

Which of the following are right triangle congruence theorems? check all that apply. a. hypotenuse-angle (ha) b. hypotenuse-leg (hl) c. leg-leg (ll) d. leg-angle (la)

Asked by maham237 @ in Mathematics viewed by 372 persons

Find the value of tan θ for the angle shown

Asked by maham237 @ in Mathematics viewed by 303 persons

A line is drawn from the origin through the point square root of thirty-three comma negative four. The angle theta is given as the measurement from the positive x axis …

State whether the given measurements determine zero, one, or two triangles. c = 30°, a = 32, c = 16

Asked by maham237 @ in Mathematics viewed by 362 persons

Find the y value for point i such that di and ei form a 3:5 ratio.

Asked by maham237 @ in Mathematics viewed by 356 persons

Find the y value for point I such that DI and EI form a 3:5 ratio. Segment DE is shown. D is at negative 3, 2. E is at 5, …

Find the x value for point c such that ac and bc form a 2:3 ratio.

Asked by maham237 @ in Mathematics viewed by 473 persons

Find the x value for point C such that AC and BC form a 2:3 ratio. Segment AB is shown. A is at negative 3, 5. B is at 3, …

Find the x value for point l such that jl and kl form a 3:1 ratio.

Asked by maham237 @ in Mathematics viewed by 342 persons

Segment JK is shown. J is at (-3, 4). K is at (4,-2). (−1.25, 2.5) (−0.5, 1) (2.25, −0.5) (0.5, 2)

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

Asked by maham237 @ in Mathematics viewed by 18347 persons

All things algebra unit 7 polygons and quadrilaterals answer key

Asked by admin @ in Mathematics viewed by 8152 persons

Gina wilson all things algebra 2016 answer key unit 11

Asked by admin @ in Mathematics viewed by 5770 persons

Unit 1 geometry basics homework 4 angle addition postulate answers

Asked by maham237 @ in Mathematics viewed by 3931 persons

Unit 6 exponents and exponential functions homework 8 answer key

Asked by maham237 @ in Mathematics viewed by 3248 persons

The manager of a vacation resort believes that the ages

Asked by maham237 @ in Mathematics viewed by 2920 persons

What is 271 403 rounded to the nearest ten thousand

Asked by maham237 @ in Mathematics viewed by 2781 persons

Unit 1 geometry basics homework 3 angle relationships answer key

Asked by maham237 @ in Mathematics viewed by 2574 persons

Homework 2 parallelograms

Asked by maham237 @ in Mathematics viewed by 2497 persons

Why would a prism beat a sphere in a competition?

Asked by maham237 @ in Mathematics viewed by 2475 persons

John wants to send a letter to peter

Asked by maham237 @ in Mathematics viewed by 2459 persons

An artist sells a painting for 20.50 but uses 5.75

Asked by maham237 @ in Mathematics viewed by 2425 persons

Unit 4 congruent triangles homework 1 classifying triangles answer key

Asked by maham237 @ in Mathematics viewed by 2415 persons

Unit 4 congruent triangles homework 2 angles of triangles

Asked by maham237 @ in Mathematics viewed by 2070 persons

Compare the values of the 2s and 5s in 55220

Asked by maham237 @ in Mathematics viewed by 1792 persons