Use a calculator to find θ to the nearest tenth of a degree, if 0° < θ < 360° and
csc(θ)=1.4307 with θ in QII
θ=?
To find the angle θ to the nearest tenth of a degree, given csc(θ) = 1.4307 and θ lies in the second quadrant (QII), you can follow these steps:
Step 1: Understand the concept
In trigonometry, csc (cosecant) is the reciprocal of sin (sine). Therefore, when csc(θ) = 1.4307, it means sin(θ) = 1/1.4307.
Step 2: Use the inverse sine function
Since we need to find the angle θ, we can use the inverse sine function (sin^(-1)) to find its value.
Step 3: Calculate the inverse sine value
Using a calculator, enter the reciprocal of 1.4307 and find its inverse sine value. The result will be the angle in radians.
Step 4: Convert radians to degrees
To get the angle in degrees, convert the radians value to degrees by multiplying it by 180/π (approximately 57.3).
Step 5: Account for QII
Since the angle lies in the second quadrant (QII), the value obtained in step 4 will not be accurate as inverse sine only gives a positive value. To account for this:
- Subtract the angle obtained in step 4 from 180 degrees to find the supplementary angle.
Step 6: Round to the nearest tenth
Finally, round the obtained angle to the nearest tenth of a degree.
By following these steps, you can find the value of θ to the nearest tenth of a degree.
To find θ to the nearest tenth of a degree, knowing that csc(θ)=1.4307 and θ is in QII, we can use a calculator to calculate the arcsine of 1/1.4307:
arcsin(1/1.4307) = 43.65°
However, since θ is in QII, we need to subtract this angle from 180°:
180° - 43.65° = 136.35°
Therefore, θ is approximately 136.4° to the nearest tenth of a degree.
if you can find θ=arccsc(1.4307), you will want 180-θ
If you can't find θ, you are in deep trouble.