Find the values of the six trigonometric functions for ∠A in standard position determined by the point (63, 280). Enter your answers as fractions.
sin A
cos A
tan A
csc A
sec A
cot A
clearly your point is in the first quadrant, so all trig ratios will be positive.
from (63,280)
x = 63, y = 280
r^2 = x^2 + y^2 = 63^2+280^2 = 82930
r = √82930
You should know the trig ratios in terms of
x, y and r
e.g.
tan A = y/x = 280/63 = 40/9
sec A = r/x = √82930/63
etc.
To find the values of the six trigonometric functions for ∠A, we need to determine the coordinates of the point (63, 280) in the coordinate plane and use them to calculate the trigonometric functions.
First, let's plot the point (63, 280) in the coordinate plane. The x-coordinate represents the horizontal distance from the origin, and the y-coordinate represents the vertical distance.
Now that we have plotted the point, we can determine the values of the trigonometric functions using the coordinates of the point.
sin A: To find sin A, divide the y-coordinate (280) by the length of the hypotenuse. The hypotenuse can be calculated using the distance formula, which is sqrt(x^2 + y^2).
sin A = y-coordinate / hypotenuse
cos A: To find cos A, divide the x-coordinate (63) by the length of the hypotenuse.
cos A = x-coordinate / hypotenuse
tan A: To find tan A, divide the y-coordinate (280) by the x-coordinate (63).
tan A = y-coordinate / x-coordinate
csc A: csc A is the reciprocal of sin A, so we can find it by taking the reciprocal of the sin A value calculated earlier.
csc A = 1 / sin A
sec A: sec A is the reciprocal of cos A, so we can find it by taking the reciprocal of the cos A value calculated earlier.
sec A = 1 / cos A
cot A: cot A is the reciprocal of tan A, so we can find it by taking the reciprocal of the tan A value calculated earlier.
cot A = 1 / tan A
Now, you can substitute the values into the formulas and calculate the exact values of the six trigonometric functions.