#!/usr/bin/env python
# coding: utf-8

# # Practice Problems
# ### Lecture 22
# Answer each number in a separate cell
# 
# Rename the notebook with your lastName, first initial and the lecture 
#     
#     ex. Cych_B_22
#     
# Turn this notebook into Canvas

# ## 1. Cartesian coordinates and polar coordinates
# - Write lambda functions to replace dir2cart() and cart2dir(). Call them **dir_cart** and **cart_dir**
# - You measured a bedding plane with an azimuth of  40 and a plunge of 62. Use your function **dir_cart()** to convert the coordinates to cartesian coordinates.
# - Use your function **cart_dir()** to convert the cartesian coordinates back to polar coordinates
# - test your functions by calling the **dir2cart()** and **cart2dir()** functions in the lecture.
# - modify **cart2dir()** to round to the nearest decimal
# 
# ## 2. Unit vectors
# - What is the sum of the two vectors Az1=245, Pl1=22 and Az2=10, Pl2=60?
# - What is the difference between these vectors?  
# - What is angle between the two vectors? 
# - What is pole to the two vectors?  
# - Make an equal angle diagram
#     - plot the two vectors as green triangles
#     - plot the pole to the plane as a blue star
#     
# ## 3.  Vectors with length
# - Modify the function **dir2cart()** from the lecture to include vector length $R$.  Call it **vec2cart()**.
# - Apply your new function to evaluate the cartesian coordinates of the vector with Azimuth=12, Plunge=42, R=8
# - Modify the function **cart2dir()** to return the full vector (Azimuth, Plunge and $R$) from the cartesian coordinates.  Call this one **cart2vec()**.  
# - Verify that your function works, by feeding the output of **dir2cart()** back into **cart2dir()** to make sure you get back what you started with.    

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