Answer:
Step-by-step explanation:
sin = opposite / hypotenuse
- sin 63° = 18/x
- x = 18 / sin 63°
- x = 20.2
The pattern is - 8 so the answer is 12.
Answer:
The solution of the equations are -6 and 1
Step-by-step explanation:
* <em>Lets explain how to solve the problem</em>
- We want to find the solution of the equation (x + 2) (x + 3) = 12
- <em>At first lets use the Foil method to multiply the two brackets</em>
(x + 2) (x + 3) = (x)(x) + (x)(3) + (2)(x) + (2)(3)
(x + 2) (x + 3) = x² + 3x + 2x + 6 ⇒ add the like term
(x + 2) (x + 3) = x² + 5x + 6
∵ (x + 2) (x + 3) = 12
∴ x² + 5x + 6 = 12
- Subtract 12 from both sides
∴ x² + 5x - 6 = 0
- <em>Factorize the left hand side</em>
∵ x² = (x)(x)
∵ -6 = 6 × -1
∵ 6x + -1x = 5x
∴ (x + 6)(x - 1) = 0
- <em>Lets use the zero product property </em>
∵ (x + 6)(x - 1) = 0
∴ x + 6 = 0 ⇒ <em>OR</em> ⇒ x - 1 = 0
∵ x + 6 = 0
- Subtract 6 from both sides
∴ x = -6
∵ x - 1 = 0
- Add 1 to both sides
∴ x = 1
∴ The solution of the equations are -6 and 1
We have that
<span>sin x=2/9
we know that
sin</span>² x+cos² x=1---------> cos² x=1-sin² x-----> cos² x=1-(2/9)²
cos² x=1-(4/81)------> (81-4)/81-----> 77/81
cos x=√(77/81)
Sin 2x = 2 sin x cos x-------> 2*(2/9)*(√(77/81))----> (4/81)*√77---> 0.43
Sin 2x=0.43
so
cos² 2x=1-sin² 2x---------> 1-[0.43]²-----> 1-[0.1878]----> 0.81
cos² 2x=0.81-----------> cos 2x=0.9
tan 2x=sin 2x/cos 2x--------> tan 2x=0.43/0.9---------> tan 2x=0.48
the answers are
sin 2x=0.43
cos 2x=0.9
tan 2x=0.48
