Yes. There is an error.chwala said:
I saw the mistake ... just wanted to counter-check myself... Cheers man!scottdave said:
What does ms stand for?chwala said:
It's chwala's abbreviation for "mark scheme."scottdave said:
To find ##\tan \theta## in the form of ##a+b\sqrt {2}##, start by expressing the angle ##\theta## in terms of known angles or using trigonometric identities. You can utilize the tangent addition formulas or double angle formulas to simplify the expression. The goal is to manipulate the expression until it matches the desired form.
Sure! For example, if ##\theta = 45^\circ + 15^\circ##, we can use the tangent addition formula: ##\tan(45^\circ + 15^\circ) = \frac{\tan 45^\circ + \tan 15^\circ}{1 - \tan 45^\circ \tan 15^\circ}##. Knowing that ##\tan 45^\circ = 1## and ##\tan 15^\circ = 2 - \sqrt{3}##, we can simplify this to find ##\tan \theta##. After simplification, it can be expressed in the form ##a + b\sqrt{2}##.
The values of ##a## and ##b## are typically real numbers. The specific values depend on the angle ##\theta## being considered. For instance, if ##\tan \theta = 1 + \sqrt{2}##, then ##a = 1## and ##b = 1##. The goal is to match the expression to the required form based on the angle's tangent value.
Yes, certain angles can yield this form. For example, angles like ##\theta = 15^\circ## or ##\theta = 75^\circ## can lead to expressions involving ##\sqrt{2}## when calculated. These angles often arise in problems involving special triangles or specific trigonometric identities.
To verify your answer, you can substitute the value of ##\tan \theta## back into the original problem or use a calculator to compute the tangent of the angle. Additionally, check if the result matches the form ##a + b\sqrt{2}## by simplifying your expression and comparing coefficients.