if sec 0= -7.3, find sin (0- pi/2).
Where is the answer
To find sin (0 - π/2), we first need to find the value of sin 0, and then substitute the value of π/2 into the negative angle.
Step 1: Find the value of sin 0
Since we know the value of sec 0 = -7.3, we can use the reciprocal relationship between sine and secant functions to find the value of sin 0. The reciprocal relationship is: sec θ = 1/cos θ. In this case, sec 0 = -7.3, so we have:
sec 0 = 1/cos 0
Multiply both sides of the equation by cos 0:
cos 0 = 1/sec 0
cos 0 = 1/(-7.3)
cos 0 = -0.136986301369863
Now, we know the value of cos 0.
Step 2: Substitute the value of π/2 into the negative angle
We need to find sin (0 - π/2). This means we need to substitute the value of π/2 into the negative angle. So, we have:
sin (0 - π/2) = sin 0 - π/2
Now, substitute the value of cos 0 into the equation:
sin (0 - π/2) = sin (cos⁻¹(-0.136986301369863) - π/2)
Use a calculator to determine the value of cos⁻¹(-0.136986301369863):
cos⁻¹(-0.136986301369863) ≈ 1.71237729056965
Now, substitute the value of cos⁻¹(-0.136986301369863) into the equation:
sin (0 - π/2) = sin (1.71237729056965 - π/2)
Use a calculator to determine the value of (1.71237729056965 - π/2):
(1.71237729056965 - π/2) ≈ -0.570796326794897
Finally, substitute the value of (1.71237729056965 - π/2) into the equation:
sin (0 - π/2) ≈ sin (-0.570796326794897)
Using a calculator, we find that sin (-0.570796326794897) is approximately -0.5365729180004346.
Therefore, sin (0 - π/2) ≈ -0.5365729180004346.
To find sin(0 - π/2), we can use the formula for the sine of the difference of two angles:
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
In this case, a = 0 and b = π/2.
Since sec(0) = -7.3, we know that cos(0) = 1/sec(0) = 1/-7.3 = -0.136986.
We also know that cos(π/2) = 0 and sin(π/2) = 1.
Using the formula, sin(0 - π/2) = sin(0)cos(π/2) - cos(0)sin(π/2)
= (0)(0) - (-0.136986)(1)
= 0 + 0.136986
= 0.136986
Therefore, sin(0 - π/2) = 0.136986.