1/tan60';sin90',tan60';...form a sequence. Calculate the fourth term.
the values are
1/√3, 1, √3, ...
I think you can see what the constant ratio is.
Square root 3
T4=1/square root3.square root 3^3 then T4=3
To calculate the fourth term of the sequence, we need to find the values of 1/tan60°, sin90°, and tan60°.
Let's start by finding the value of tan60°.
To do this, we need to know the trigonometric identity that states: tan(θ) = sin(θ)/cos(θ).
In this case, θ is equal to 60 degrees, so we can substitute θ with 60° in the equation:
tan(60°) = sin(60°)/cos(60°).
The value of sin(60°) can be found using the trigonometric identity: sin(60°) = √3/2.
Similarly, the value of cos(60°) can be found using the trigonometric identity: cos(60°) = 1/2.
Substituting these values into the equation, we get:
tan(60°) = (√3/2) / (1/2)
Simplifying further, we have:
tan(60°) = (√3/2) * (2/1)
tan(60°) = √3
Now that we know the value of tan(60°), let's move on to finding the value of sin(90°).
The value of sin(90°) is a well-known trigonometric value, which is equal to 1.
Finally, we have all the values we need to calculate the fourth term of the sequence.
The sequence stated is: 1/tan60°, sin90°, tan60°.
Therefore, the fourth term of the sequence is tan60°, which we found to be √3.