First, tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>), so if cos(<em>θ</em>) = 3/5 > 0 and tan(<em>θ</em>) < 0, then it follows that sin(<em>θ</em>) < 0.
Recall the Pythagorean identity:
sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1
Then
sin(<em>θ</em>) = -√(1 - cos²(<em>θ</em>)) = -4/5
and so
tan(<em>θ</em>) = (-4/5) / (3/5) = -4/3
The remaining trig ratios are just reciprocals of the ones found already:
sec(<em>θ</em>) = 1/cos(<em>θ</em>) = 5/3
csc(<em>θ</em>) = 1/sin(<em>θ</em>) = -5/4
cot(<em>θ</em>) = 1/tan(<em>θ</em>) = -3/4
Answer:
- The value of x is 12 units.
Step-by-step explanation:
<u>We know that:</u>
<u>Let's solve using Pythagoras theorem.</u>
- => 13² = 5² + x²
- => 169 = 25 + x²
- => 169 - 25 = x²
- => 144 = x²
- => √x² = √144
- => x = √144
- => x = 12
Hence, the value of x is 12 units.
You end up at the point (5, 5).
20/35 and 21/35. The common denominator is 35.