cos t=.7, tan t<0. find the values of the other 5 trigonometric functions.
draw the triangle: adjacent+.7, hypo, 1.0, opposite -.51
Tant=.51/.70, sint=-.51/1.0, and so on.
are you meant t is negative?
cost >0 and tant< 0 , then t is in IV
if cos t = .7 = 7/10, then my triangle is 7 - √51 - 10
sint = -√51/10 , csc t = -10/√51
cos t = 7/10, sec t = 10/7
tan t = -V51/7 , cot t = -7/√51
To find the values of the other five trigonometric functions, we need to use the given information that cos(t) = 0.7 and tan(t) < 0.
1. Start by drawing a right triangle in the coordinate plane. Since tan(t) < 0, we know that t is an angle in either the second or fourth quadrant.
2. Let's assume t is in the second quadrant. In this case, the adjacent side of the triangle will be negative, and the opposite side will be positive.
3. Since cos(t) = adjacent/hypotenuse, we can substitute the given value and solve for the adjacent side. In this case, adj/hyp = 0.7. Let's assume the hypotenuse is 1, so the adjacent side is 0.7.
4. Now, we can use the Pythagorean theorem to find the opposite side. Since the hypotenuse is 1 and the adjacent side is 0.7, we can solve for the opposite side using the equation opposite^2 = hypotenuse^2 - adjacent^2. Plugging in the values, we get opposite^2 = 1^2 - 0.7^2 = 0.51. Taking the square root, we find that the opposite side is approximately 0.71.
5. Next, we can find the values of the other trigonometric functions:
- sin(t) = opposite/hypotenuse = 0.71/1 = 0.71
- csc(t) = 1/sin(t) = 1/0.71 ≈ 1.41
- sec(t) = 1/cos(t) = 1/0.7 ≈ 1.43
- cot(t) = 1/tan(t) = -1/(tan(t)) (since tan(t) < 0) = approximately -1/tan(t)
- To find cot(t), we can use the trigonometric identity cot(t) = 1/tan(t). However, since tan(t) < 0, we can write cot(t) = -1/tan(t).
- Let's say that tan(t) = x. Then, cot(t) = -1/x.
6. So, the values of the other five trigonometric functions when cos(t) = 0.7 and tan(t) < 0 are approximately:
- sin(t) ≈ 0.71
- csc(t) ≈ 1.41
- sec(t) ≈ 1.43
- cot(t) ≈ -1/tan(t) (which is approximately -1/x, where x is the value of tan(t) which we are not given)
Please note that these values are approximate due to rounding. If you want more precise values, you can use a calculator to calculate them.