(3 cos x-4 sin x)+(3sin x+4 cos x)=5
(3cos x+4cos x)+(-4sin x+3 sin x)=5
7 cos x-sin x=5
7cos x=5+sin x
(7 cos x)²=(5+sinx)²
49 cos²x=25+10 sinx+sin²x
49(1-sin²x)=25+10 sinx+sin²x
49-49sin²x=25+10sinx+sin²x
50 sin² x+10sinx-24=0
Sin x=[-10⁺₋√(100+4800)]/100=(-10⁺₋70)/100
We have two possible solutions:
sinx =(-10-70)/100=-0.8
x=sin⁻¹ (-0.8)=-53.13º (360º-53.13º=306.87)
sinx=(-10+70)/100=0.6
x=sin⁻¹ 0.6=36.87º
The solutions when 0≤x≤360º are: 36.87º and 306.87º.
Reorder 2 cos (2y) and sin (2y)
= sin (2y)(2 cos(2y))
Remove parenthesis
= sin (2y) * 2 cos (2y)
Reorder sin (2y) and 2
= 2 * sin (2y) cos (2y)
Apply the sine double-angle identity
= sin (2(2y))
Now multiply 2 by 2
<u>= sin (4y) </u>
All you have to do is do the distributive property. So, for the first one you would do 5 times x which equals 5x and then you would do 5 times 4 which equals twenty. All you are left with is the addition sign. Your full equation now would be 5x+20
The circumference would be 18.85
Answer:
5,418.2 feet
Step-by-step explanation:
Nadia is carrying out mountain climbing.
She started climbing the mountain at an altitude of 19.26 feet below the sea level.
Nadia changed her altitude by climbing a total of 5,437.8 feet from her starting position.
Therefore, Nadia's altitude at the end of her climb can be calculated as follows
= 5,437.8-19.6
= 5,418.2
Hence Maria's altitude at the end of her climb is 5,418.2 feet
