Solving Trigonometic Equations
1)sinx = (4/5)
2) cosx = (-12/13)
Solving Trigonometic Equations
1)sinx = (4/5)
2) cosx = (-12/13)
What is the question? Solve for x?
x= arcsin (4/5) put that in your calculator.
Same for the next.
For both cases I recognize the sides of well-known right-angled triangles: {3,4,5} and {5,12,13}
As bobpursley said, you did not ask what should be done.
One type of question would be to give the other 2 trig ratios for acute angles, or
find all solutions for the angle x in a given domain.
There should be detailed and fully explained example of this type of question in your text book
Did they teach you a memory aid called CAST ? It makes this topic very easy
Solve for x , please
To solve the trigonometric equations, we need to find the values of x that satisfy the given equations.
1) sinx = 4/5:
To solve this equation, we can use the arc sine function (also known as inverse sine or sin^-1). Taking the inverse sine of both sides of the equation:
arcsin(sinx) = arcsin(4/5)
Since arcsin and sinx are inverse operations of each other, they cancel out:
x = arcsin(4/5)
Now, you can calculate the value of arcsin(4/5) using a scientific calculator, which will give you the solution in radians. Make sure your calculator is set to the appropriate mode (either degrees or radians) depending on the required unit for the solution.
2) cosx = -12/13:
Similarly, to solve this equation, we can use the arc cosine function (also known as inverse cosine or cos^-1). Taking the inverse cosine of both sides of the equation:
arccos(cosx) = arccos(-12/13)
Again, since arccos and cosx are inverse operations, they cancel out:
x = arccos(-12/13)
Calculate the value of arccos(-12/13) using a scientific calculator in radians or degrees, based on the required unit of the solution.
Keep in mind that there may be multiple solutions to trigonometric equations, so if you need to find all solutions within a certain domain or interval, you may have to consider additional steps or restrictions. Check your textbook or instructor's guidance for specific requirements and examples.