Answer: 0, π, 2π
Nevertheless, that is not an option. I see two possibilities: 1) the options are misswirtten, 2) the domain is not well defined.
If the domain were 0 ≤ θ < 2π, then 2π were excluded of the domain ant the answer would be 0, π.
Explanation:
1) The first solution, θ = 0 is trivial:
sin (0) - tan (0) = 0
0 - 0 = 0
2) For other solutions, work the expression:
sin(θ) + tan (-θ) = 0 ← given
sin (θ) - tan(θ) = 0 ← tan (-θ) = tan(θ)
sin(θ) - sin (θ) / cos(θ) = 0 ← tan(θ) = sin(θ) / cos(θ)
sin (θ) [1 - 1/cos(θ)] = 0 ← common factor sin(θ)
⇒ Any of the two factors can be 0
⇒ sin (θ) = 0 or (1 - 1 / cos(θ) = 0,
sin(θ) = 0 ⇒ θ = 0, π, 2π
1 - 1/cos(θ) = 0 ⇒ 1/cos(θ) = 1 ⇒ cos(θ) = 1 ⇒ θ = 0, 2π
⇒ Solutions are 0, π, and 2π
In fact if you test with any of those values the equation is checked. The only way to exclude one of those solutions is changing the domain.
Answer:
Step-by-step explanation:
1 hr=60 min
1 km=0.62137 miles
15 km/min=(15×60) km/hr=900 km/hr=(900×0.62137) miles /hr=559.233 miles/hr
Answer:
<h2>5, 7, 11</h2>
Step-by-step explanation:
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
A prime number has only two divisors: 1 and itself.
Therefore, the prime numbers are:
5, 7 and 11.
12 is not a prime because 12 = 2 × 6 = 3 × 4.
12 has six divisors: 1, 2, 3, 4, 6 and 12.
Answer:
Fraction: 10 and 5/8
Step-by-step explanation:
17 × 5/8
85/8
