function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.) Build new functions from existing functions. Find inverse functions. Verify by composition that one function is the inverse of another. Read values of an inverse function from a graph or a table, given that the function has an inverse. Produce an invertible function from a non-invertible function by restricting the domain. Understand the inverse relationship between exponents and logarithms and use this relationship to problems involving logarithms and exponents. Extend the domain of trigonometric functions using the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for and and use the unit circle to express π/3, π/4 π/6, the values of sine, cosine, and tangent for and 2π–x in of π–x, π+x, their values for x, where x is any real number. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Model periodic phenomena using trigonometric functions. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Prove and apply trigonometric identities. Prove the addition and subtraction formulas for sine, cosine and tangent
function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.) Build new functions from existing functions. Find inverse functions. Verify by composition that one function is the inverse of another. Read values of an inverse function from a graph or a table, given that the function has an inverse. Produce an invertible function from a non-invertible function by restricting the domain. Understand the inverse relationship between exponents and logarithms and use this relationship to problems involving logarithms and exponents. Extend the domain of trigonometric functions using the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in of their values for x, where x is any real number. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Model periodic phenomena using trigonometric functions. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Prove and apply trigonometric identities. Prove the addition and subtraction formulas for sine, cosine and tangent